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Matching Equations and Graphs

1.10.4 Matching Equations and Graphs

1.10.4 • Matching Equations and Graphs

Cool Down

Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1.

1.

Write an equation to represent the relationship between the dollar amount Kiran is spending and the number of games, x x , and the number of rides, y y , he could do.

Compare your answer:

0.25 x + y = 12 0.25 x + y = 12

2.

Which graph represents the relationship between the quantities in this situation?

A. Line graph showing a positive correlation between the number of games on the x-axis (0 to 18) and the number of rides on the y-axis (0 to 18), with the line increasing steadily.
B. A line graph with number of games on the x-axis and number of rides on the y-axis. The line starts at (0, 12) and drops steeply to (3, 0), then remains at zero.
C. A line graph showing number of rides on the y-axis and number of games on the x-axis. The line slopes downward from about 12 rides at 0 games to about 8 rides at 16 games.

Compare your answer:

Graph C (for y = 12 − 14 x y = 12 − 14 x )

3.

Explain how you determined your answer to the previous question.

Compare your answer: Your answer may vary, but here are some samples.

  • If Kiran plays 0 games, he could get on 12 rides. If he gets on 0 rides, he could play 48 games. Both the points (0,12) and (48,0) are on the line in Graph C.
  • Rearranging the equation into slope-intercept form gives y = 12 − 1 4 x y = 12 − 1 4 x , so the graph has a slope of − 1 4 − 1 4 and intersects the y y -axis at 12, which matches Graph C.