Grade 8 Workbook — Chapter 8: Linear Functions and $y = mx + b$

SOL 8.PFA.3 · Companion to Textbook Chapter 8

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Every numbered item is the same problem as in the textbook, so one answer key serves both. Item numbers run continuously from 1 to 172.

Blank coordinate grids: fig11-blank-grids.png holds four labeled grids from $-6$ to $6$ on both axes. Paste one grid per graphing item, or the full sheet where four graphs are requested on one page.

PAGE 1 — Chapter opener

Chapter 8 · Linear Functions and $y = mx + b$

Standard 8.PFA.3

In this chapter you will:

• See what adding a constant $b$ does to the proportional line $y = mx$
• Name the slope, the y-intercept, and the independent and dependent variables
• Graph a linear function from an equation, a table, or a story
• Build a table of values from an equation, a graph, or a story
• Write $y = mx + b$ from a graph, a table, or a story
• Invent a real-world story for a linear function you are handed

Words to know: proportional relationship · linear function · slope-intercept form · slope $m$ · rate of change · rise · run · y-intercept $b$ · translation · parallel · independent variable · dependent variable · table of values · lattice point · x-intercept · context

Integer rule for this whole chapter: the y-intercept $b$ and the coordinates of every point you plot are integers. The slope $m$ may be a fraction.

PAGE 2 — Adding a constant slides the line

8.1 Translating $y = mx$

FIGURE: fig1-translating-y-equals-2x.png (full width)

Fill in the blanks.

The equation $y = mx$ graphs a line through the ______________.

Adding a positive constant $b$ slides the line ______________ by ______ units.

Adding a negative constant slides the line ______________.

A vertical translation does not change the ______________, so the lines are ______________.

The line $y = mx + b$ always passes through the point ( ______ , ______ ).

FIGURE: fig2-same-slope-different-intercepts.png (full width)

1. The graph of $y = 3x$ is translated up $5$ units.

   Description: _______________________________________________

   Equation: _______________

2. How is the graph of $y = -x - 6$ related to the graph of $y = -x$?

   ---

3. What proportional line was translated to give $y = \tfrac{1}{2}x + 4$, and how far?

   Parent line: _______________ Translation: _______________

PAGE 3 — Translation practice

Parent Lines and Translations

4. Translate $y = 4x$ down $7$ units. Equation: _______________

5. Does a vertical translation change the slope? _______

   Why? _______________________________________________

6. y-intercept of $y = 2x - 9$ as an ordered pair: ( ______ , ______ )

7. Complete the table.

8. Translate $y = -3x$ up $4$ units. Equation: _______________

9. Translate $y = \tfrac{1}{4}x$ down $3$ units. Equation: _______________

10. In the figure on page 2, which line is highest at $x = 1$?

    Line: _______________ Ordered pair that shows it: ( ______ , ______ )

11. How far apart vertically are $y = 2x + 3$ and $y = 2x - 4$?

    Show the subtraction: _______________________________________________

    Does the distance depend on $x$? _______

PAGE 4 — Tables and reasoning about translation

Two Columns, One Slide

12. Complete the table, then say how the two output columns are related.

Relationship: _______________________________________________

13. Is $y = 2x + 3$ proportional? _______ Give two reasons.

    Reason one: _______________________________________________

    Reason two: _______________________________________________

14. Reasoning. Why do the graphs of $y = \tfrac{1}{2}x + 3$ and $y = \tfrac{1}{2}x - 2$ never meet?

    ---

    ---

15. Application. A pool filling from empty at $2$ inches per hour was $y = 2x$. Today it already holds $6$ inches before the hose starts.

    New equation: _______________

    What happened to the graph? _______________________________________________

16. Error analysis. A student says $y = 3x - 5$ is $y = 3x$ translated $5$ units to the left.

    The error: _______________________________________________

    The correct translation: _______________________________________________

Exit ticket 8.1

17. Translate $y = 6x$ up $2$ units. _______________

18. $y = -x - 7$: parent line _______________ translation _______________

19. y-intercept of $y = \tfrac{3}{5}x + 4$: ( ______ , ______ )

20. Why can a vertical translation never change the slope?

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PAGE 5 — The four key characteristics

8.2 Key Characteristics of a Linear Function

FIGURE: fig3-key-characteristics.png (right half, full height)

Fill in the blanks.

Slope-intercept form: $y = \underline{\hspace{2cm}}x + \underline{\hspace{2cm}}$

$m$ is the ______________, equal to $\dfrac{\text{rise}}{\text{run}}$.

$b$ is the ______________, the $y$-coordinate of the point ( ______ , ______ ).

$x$ is the ______________ variable — the input.

$y$ is the ______________ variable — the output.

For the graphed line: $m =$ ______ and $b =$ ______.

FIGURE: fig5-slope-directions.png (full width)

If $m > 0$ the line ______________. If $m < 0$ the line ______________. If $m = 0$ the line is ______________.

21. $y = 4x - 1$: $m =$ ______ $b =$ ______

22. $y = -\tfrac{2}{3}x + 5$: $m =$ ______ $b =$ ______

23. Taxi cost depends on miles driven. Independent variable: _______________

24. Does $y = -x + 8$ rise or fall? _______ Which characteristic decides? _______________

25. y-intercept of $y = 7x$: ( ______ , ______ )

26. Slope of $y = 0x + 3$: ______ Its graph looks like: _______________________________________________

PAGE 6 — Naming $m$ and $b$ reliably

Reading the Two Numbers

27. Complete the table.

28. From the graph of $y = 2x - 3$ on page 5:

    $m =$ ______ $b$ as an ordered pair: ( ______ , ______ )

    Three other points on the line: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

29. Rises, falls, or level?

30. Which is steeper, $y = 3x + 1$ or $y = \tfrac{1}{2}x + 1$? _______________

    Justify with rise and run: _______________________________________________

31. A phone plan costs $y = 4x + 20$ dollars for $x$ gigabytes.

    Independent variable: _______________ Dependent variable: _______________

    $m =$ ______ meaning _______________________________________________

    $b =$ ______ meaning _______________________________________________

PAGE 7 — Reasoning about the characteristics

What Each Number Controls

32. Reasoning. Two linear functions have the same y-intercept but different slopes.

    Must have in common: _______________________________________________

    Must differ: _______________________________________________

33. Reasoning. Why does a linear function have exactly one y-intercept? Use $y = mx + b$.

    ---

34. $y = -2x + 5$: $m =$ ______ $b =$ ______

    What the negative slope tells you: _______________________________________________

35. Application. A lawn service charges $12 to show up plus $9 per hour.

    Equation: _______________ $m =$ ______ $b =$ ______

    Independent variable: _______________ Dependent variable: _______________

36. Error analysis. For $y = 8 - 3x$ a student writes $m = 8$, $b = -3$.

    The error: _______________________________________________

    Correct values: $m =$ ______ $b =$ ______

Exit ticket 8.2

37. $y = -\tfrac{1}{3}x + 6$: $m =$ ______ $b =$ ______

38. $y = 12 - 5x$: $m =$ ______ $b =$ ______

39. Distance traveled depends on driving time. Dependent variable: _______________

    Why? _______________________________________________

40. What does the slope tell you that the y-intercept does not?

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PAGE 8 — Graphing in two moves

8.3 Graphing from an Equation

FIGURE: fig4-graphing-from-equation.png (full width)

The two steps.

Step 1: plot the point ( ______ , ______ ).

Step 2: from there, move right by the ______________ and up or down by the ______________.

Remember: $m = 3$ means $\dfrac{3}{\underline{\hspace{1cm}}}$, so right ______ and up ______.

Graph each function. Plot $b$ first, then use $m$. List three integer points under each grid.

41. $y = 2x - 3$

    GRID: fig11-blank-grids.png, Grid A (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

42. $y = -x + 4$

    GRID: fig11-blank-grids.png, Grid B (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

43. $y = \tfrac{1}{2}x + 1$

    GRID: fig11-blank-grids.png, Grid C (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

44. $y = -\tfrac{3}{2}x + 4$

    GRID: fig11-blank-grids.png, Grid D (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

PAGE 9 — More graphing

Graphing Practice

45. $y = 3x$

    GRID: blank coordinate grid, $-6$ to $6$ both axes (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

46. $y = -4$

    GRID: blank coordinate grid, $-6$ to $6$ both axes (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

47. $y = \tfrac{2}{3}x - 2$

    GRID: blank coordinate grid, $-6$ to $6$ both axes (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

48. $y = -2x + 5$

    GRID: blank coordinate grid, $-6$ to $6$ both axes (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

49. $y = \tfrac{1}{4}x + 3$ — one point left of the $y$-axis, one right

    GRID: blank coordinate grid, $-8$ to $8$ on x, $-6$ to $6$ on y (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

50. $y = -\tfrac{1}{2}x - 1$ — one point on each side of the $y$-axis

    GRID: blank coordinate grid, $-6$ to $6$ both axes (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

PAGE 10 — Graphing applications

Graphs That Mean Something

51. $y = 5x - 6$

    GRID: blank coordinate grid, $-6$ to $6$ on x, $-8$ to $8$ on y (half width)

    Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

52. Graph $y = x + 2$ and $y = x - 3$ on one grid.

    GRID: blank coordinate grid, $-6$ to $6$ both axes (full width)

    How the lines are related: _______________________________________________

    Distance apart: ______ units

53. Reasoning. Why is plotting $b$ first faster than building a whole table?

    ---

54. Application. A candle is $12$ cm tall and burns $2$ cm per hour.

    Equation: _______________

    GRID: first-quadrant grid, x from 0 to 6, y from 0 to 12

    What $(6, 0)$ means: _______________________________________________

55. Application. A taxi charges $3 plus $2 per mile.

    Equation: _______________

    GRID: first-quadrant grid, x from 0 to 6, y from 0 to 16

    Cost of a $5$-mile ride, read from the graph: $______

56. Error analysis. To graph $y = -3x + 2$ a student went right $3$ and down $1$ from $(0, 2)$.

    Slope the student actually used: ______

    The correct move: _______________________________________________

Exit ticket 8.3

57. Graph $y = 3x - 4$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

58. Graph $y = -\tfrac{2}{3}x + 2$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

59. Graph $y = \tfrac{1}{2}x - 3$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

GRID: fig11-blank-grids.png (full sheet — use Grids A, B, C for items 57–59)

60. How does the sign of $m$ tell you which way to move after plotting $b$?

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PAGE 11 — Tables from equations

8.4 Tables of Values

FIGURE: fig6-table-to-graph.png (full width)

Fill in the blanks.

The row where $x = 0$ shows the value of ______.

If $x$ goes up by $1$ each row, then $y$ goes up by ______ each row.

For a fractional slope, choose $x$-values that are multiples of the ______________ of $m$.

61. $y = 4x - 1$

62. $y = -2x + 6$

63. $y = \tfrac{1}{2}x + 2$

64. Read the graph of $y = 3x - 2$ above and fill in its table.

65. $y = -x + 3$

66. If the $x$-values go up by $1$ each row, what must be true of the $y$-values?

    _______________________________________________ Characteristic involved: ______________

PAGE 12 — Choosing $x$-values on purpose

Tables You Can Actually Plot

67. $y = 3x + 2$

Constant change in $y$: ______

68. $y = -\tfrac{3}{2}x + 4$

69. $y = \tfrac{2}{3}x - 1$ — choose four $x$-values that give integer $y$.

How you chose them: _______________________________________________

70. $y = 6$

Slope: ______ How the table shows it: _______________________________________________

71. Read four ordered pairs from the graph of $y = -2x + 5$ (page 13).

PAGE 13 — Tables from contexts

Tables from Stories

72. Bike rental: $5 plus $3 per hour, so $y = 3x + 5$.

73. A $20$-liter tank drains $4$ liters per minute, so $y = -4x + 20$.

What the last column means: _______________________________________________

74. Reasoning. Is this table linear? $x = 0, 1, 2, 3$ and $y = 1, 3, 6, 10$.

Changes in $y$: ______ , ______ , ______ Linear? _______

The test you used: _______________________________________________

75. Application. A saver starts with $25 and adds $10 a week.

Equation: _______________

Week the total reaches $85: ______

76. Error analysis. For $y = \tfrac{1}{3}x + 2$ a student chose $x = 1, 2, 4, 5$ and got non-integer outputs.

Why: _______________________________________________

Four better $x$-values: ______ , ______ , ______ , ______

Exit ticket 8.4

77. $y = 5x - 3$ at $x = -1, 0, 1, 2$: ______ , ______ , ______ , ______

78. $y = -x - 4$ at $x = -2, 0, 2$: ______ , ______ , ______

79. Four $x$-values giving integer $y$ for $y = \tfrac{3}{4}x + 1$:

80. How can you find $b$ directly from a table? _______________________________________________

PAGE 14 — Reading an equation off a graph

8.5 Writing $y = mx + b$

FIGURE: fig7-graph-to-equation.png (right half, full height)

Fill in the blanks.

Read $b$ where the line crosses the ______________-axis.

Pick two ______________ points — points at grid corners — and count $m = \dfrac{\underline{\hspace{1.5cm}}}{\underline{\hspace{1.5cm}}}$.

Counting down gives a ______________ rise; counting left gives a ______________ run.

For the graphed line: $b =$ ______ , rise ______ , run ______ , so $m =$ ______ and the equation is _______________.

81. Equation of the graphed line: _______________

82. A line crosses at $(0, -3)$ and passes through $(1, -1)$. Equation: _______________

83. $x = 0, 1, 2, 3$ and $y = 4, 7, 10, 13$.

    $m =$ ______ $b =$ ______ Equation: _______________

84. $x = 0, 1, 2, 3$ and $y = 9, 7, 5, 3$.

    $m =$ ______ $b =$ ______ Equation: _______________

85. Through $(0, -1)$ and $(2, 3)$. Equation: _______________

86. $x = 0, 2, 4, 6$ and $y = 5, 6, 7, 8$.

    $m =$ ______ $b =$ ______ Equation: _______________

PAGE 15 — Equations from points and tables

From Two Points, From Four Rows

87. Write the equation through each pair of points.

88. $x = -1, 0, 1, 2$ and $y = -7, -4, -1, 2$. Equation: _______________

89. $x = -2, 0, 2, 4$ and $y = 9, 6, 3, 0$. Equation: _______________

90. $x = 1, 2, 3, 4$ and $y = 1, 3, 5, 7$. Equation: _______________

    How you found $b$ with no $x = 0$ row: _______________________________________________

91. $x = 2, 4, 6, 8$ and $y = -1, -2, -3, -4$. Equation: _______________

    Proportional? _______ Why? _______________________________________________

92. Slope $-3$ through $(0, 7)$. Equation: _______________

PAGE 16 — Equations from stories

Stories to Equations

93. Application. A printing shop charges $8 setup plus $2 per shirt.

    Equation: _______________ Cost of $15$ shirts: $______

94. Application. A tank holds $24$ gallons and loses $3$ gallons per minute.

    Equation: _______________ Minutes until empty: ______

95. Reasoning. One student counts between $(0, 4)$ and $(2, 6)$; another between $(2, 6)$ and $(6, 10)$.

    First slope: ______ Second slope: ______ Equation both get: _______________

    Why it had to happen: _______________________________________________

96. Error analysis. From $x = 0, 1, 2$ and $y = 5, 8, 11$ a student writes $y = 5x + 3$.

    The error: _______________________________________________

    Correct equation: _______________

Exit ticket 8.5

97. Slope $4$ through $(0, -2)$: _______________

98. $x = 0, 3, 6$ and $y = -1, 1, 3$: _______________

99. Through $(0, 5)$ and $(1, 1)$: _______________

100. How do you find $b$ from a table with no $x = 0$ row?

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PAGE 17 — What the numbers mean in a story

8.6 Linear Functions in Context

FIGURE: fig8-context-bike-rental.png (full width)

Fill in the blanks.

$b$ is the ______________ amount — the value of $y$ when $x =$ ______.

$m$ is the ______________ — how much $y$ changes for each one unit of $x$.

A quantity measured "per" something is ______; a one-time quantity is ______.

101. In $y = 3x + 5$: $b =$ ______ meaning _______________________________________________

102. $m =$ ______ meaning _______________________________________________

103. Cost of $7$ hours: $______ Show the substitution: _______________

FIGURE: fig9-context-draining-tank.png (full width)

104. What $(5, 0)$ means: _______________________________________________

105. Lawn service: $12 to show up plus $9 per hour. Equation: _______________

106. Independent variable: _______________ Dependent variable: _______________

PAGE 18 — Four representations of one story

Equation, Table, Graph, Answer

107. A gym charges $20 to join plus $12 per month.

     a) Equation: _______________

     b) Table

 c) Total after $10$ months: \$______

108. A drone hovers at $30$ m and descends $6$ m per second.

     a) Equation: _______________

     b) Table

 c) It reaches the ground at $x =$ ______

109. A book club has $4$ members and adds $2$ per week.

     Equation: _______________

     GRID: first-quadrant grid, x from 0 to 6, y from 0 to 18

     Members after $6$ weeks: ______

110. A taxi charges $3 plus $2 per mile.

 Which column holds the independent variable? _______________

PAGE 19 — Interpreting and comparing

Reading Stories off Graphs

111. From the bike-rental graph, cost of $4$ hours: $______

     Confirm with the equation: _______________

112. Reasoning. Why does $x = -2$ not make sense in the bike-rental story?

     ---

113. Reasoning. Plans $y = 5x + 10$ and $y = 5x + 25$.

     Always more expensive: _______________ By how much: $______

     What the two graphs look like together: _______________________________________________

114. Application. A phone plan costs $30 per month plus $5 per gigabyte.

     Equation: _______________

 Bill for $9$ GB: \$______

115. Application. A candle is $15$ cm tall and burns $3$ cm per hour.

     Equation: _______________ Height after $4$ hours: ______ cm Burns out at $x =$ ______

116. Error analysis. For "a $6 handling fee plus $4 per package," a student writes $y = 6x + 4$.

     Correct equation: _______________

     The test that tells you which number multiplies $x$: _______________________________________________

Exit ticket 8.6

117. A pool holds $10$ inches and rises $4$ inches per hour. Equation: _______________

118. Table for item 117:

119. What the y-intercept means: _______________________________________________

120. How do you decide which number is $m$ and which is $b$?

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PAGE 20 — Inventing a story

8.7 Creating a Context

FIGURE: fig10-create-a-context.png (full width)

The four questions.

• Question one. What does $x$ ______________?
• Question two. What does $y$ ______________?
• Question three. What is $b$ — the amount of $y$ that already exists when $x =$ ______?
• Question four. What is $m$ — the amount added for each ______ more of $x$?

Then check by substituting one value and reading the result as a sentence.

For each item write your story in complete sentences, and label what $x$ counts, what $y$ measures, and what $b$ and $m$ mean.

121. $y = 5x + 20$

     $x$ counts: _______________ $y$ measures: _______________

     Story: _______________________________________________

     ---

     Check at one value: _______________

122. $y = -2x + 16$ — must describe something decreasing.

     Story: _______________________________________________

     ---

123. For $y = 10x + 50$, a real-world quantity $b = 50$ could be:

     ---

124. For $y = -3x + 12$, what the negative slope must mean:

     ---

125. Using the graph above ($y = 2x + 6$), write a story and check it at one value of $x$.

     Story: _______________________________________________

     Check: _______________

126. Why must any context for $y = 4x + 7$ involve something that starts at $7$?

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PAGE 21 — Contexts from equations, tables, and graphs

More Stories

127. Write a context for each.

128. Table: $x = 0, 1, 2, 3$ and $y = 12, 15, 18, 21$.

     Equation: _______________ Story: _______________________________________________

129. A line through $(0, 9)$ with slope $-3$.

     Equation: _______________ Story: _______________________________________________

     What the $x$-intercept means: _______________________________________________

130. $y = 6x + 2$. Story: _______________________________________________

     What happens at $x = 5$: _______________________________________________

131. Two different contexts for $y = 25x + 100$.

     Money story: _______________________________________________

     Non-money story: _______________________________________________

PAGE 22 — Reasoning about contexts

Making the Story Fit the Numbers

132. Reasoning. Why must a context for $y = -4x + 20$ describe something that runs out?

     _______________________________________________ It runs out at $x =$ ______

133. Reasoning. "A car travels $60$ miles per hour" fits $y = 60x$. What must be added to the story for $y = 60x + 5$?

     ---

134. Application. Context for $y = 2x + 6$: _______________________________________________

     What $(4, 14)$ means: _______________________________________________

135. Application. Context for $y = -\tfrac{1}{2}x + 10$ with $x$ in days:

     ---

     What happens at $x = 20$: _______________________________________________

136. Error analysis. For $y = 7x + 15$: "A gym charges $7 to join and $15 each month."

     The error: _______________________________________________

     Corrected context: _______________________________________________

Exit ticket 8.7

137. Context for $y = 9x + 5$: $x$ = _______________ $y$ = _______________

     ---

138. Context for $y = -6x + 30$: _______________________________________________

     What the $x$-intercept means: _______________________________________________

139. In your item 137 story, what does $(3, 32)$ mean? _______________________________________________

140. The two questions to ask first: 1. _______________ 2. _______________

PAGE 23 — Review Parts A and B

Chapter 8 Review · Translation and Key Characteristics

Part A — Adding a constant translates $y = mx$

141. $y = 5x - 3$ compared to $y = 5x$: _______________________________________________

142. $y = -2x$ translated up $6$: _______________

143. Why $y = \tfrac{1}{2}x + 3$ and $y = \tfrac{1}{2}x - 2$ are parallel: _______________________________________________

144. Complete the table.

 Relationship between the columns: _______________________________________________

145. A vertical translation changes ______________ and not ______________. Why? _______________

Part B — Key characteristics

146. Name $m$ and $b$.

147. $y = -x + 9$ rises or falls? _______________

148. Gasoline left depends on miles driven. Independent: _______________ Dependent: _______________

149. Steeper: $y = \tfrac{2}{3}x - 1$ or $y = 2x - 1$? _______________ Why? _______________

150. What $b$ tells you, and the ordered pair it names: _______________________________________________

PAGE 24 — Review Parts C and D

Chapter 8 Review · Graphs and Tables

Part C — Graphing

GRID: fig11-blank-grids.png (full sheet — Grids A–D for items 151–153 and 155)

151. $y = 2x - 5$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

152. $y = -\tfrac{1}{3}x + 2$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

153. $y = -4x + 3$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

154. A jug holds $4$ liters; a pump adds $2$ liters per minute.

     Equation: _______________

     GRID: first-quadrant grid, x from 0 to 5, y from 0 to 14

155. $y = \tfrac{3}{2}x - 3$. Points: ( ___ , ___ ) ( ___ , ___ ) ( ___ , ___ )

Part D — Tables

156. $y = -5x + 4$

157. $y = \tfrac{1}{4}x - 2$ — choose four $x$-values giving integer $y$.

158. $y = 2x - 4$

159. Is $x = 0, 1, 2, 3$ with $y = 2, 4, 8, 16$ linear? _______ Test used: _______________

PAGE 25 — Review Parts E, F, and G

Chapter 8 Review · Equations, Contexts, Mixed

Part E — Writing $y = mx + b$

160. Through $(0, 7)$ and $(2, 1)$: _______________

161. $x = 0, 4, 8$ and $y = -3, -1, 1$: _______________

162. $x = 3, 4, 5, 6$ and $y = 11, 14, 17, 20$: _______________

163. A well holds $18$ gallons; a pump removes $2$ gallons per hour.

     Equation: _______________ Empty at $x =$ ______

164. Slope $6$ through $(0, -8)$: _______________

Part F — Creating a context

165. $y = 15x + 40$: $x$ = _______________ $y$ = _______________

     Story: _______________________________________________

     $m$ means _______________ $b$ means _______________

166. $y = -7x + 35$: Story: _______________________________________________

     What the $x$-intercept means: _______________________________________________

167. Table $x = 0, 1, 2, 3$ and $y = 8, 11, 14, 17$.

     Equation: _______________ Story: _______________________________________________

168. $y = \tfrac{1}{3}x + 2$ with $x$ in days: _______________________________________________

Part G — Mixed

169. $y = -3x + 12$. $m =$ ______ $b =$ ______

 `GRID: first-quadrant grid, x from 0 to 5, y from 0 to 14`

 Related to $y = -3x$ how? _______________________________________________

170. $y = 4x - 6$ four ways.

     Equation: _______________

 `GRID: blank coordinate grid, $-6$ to $6$ on x, $-8$ to $8$ on y`

 Context: _______________________________________________

171. Error analysis. A student graphs $y = \tfrac{2}{3}x + 1$ by going up $3$ and right $2$ from $(0, 1)$.

     Slope actually used: ______ Correct first step: _______________________________________________

172. Reasoning. Two functions have slope $2$; one passes $(0, 3)$, the other $(0, -4)$.

     Comparison: _______________________________________________

     Translation mapping the first onto the second: _______________________________________________