Slope-Intercept Form — Quiz

Question 5 • Mathematics 8

Samantha’s parents give her $10 per week. For each chore that she does not complete, she must repay her parents $1. Which graph models Samantha’s allowance?

Answer

Image with description A line graph on a Cartesian coordinate plane showing a linear relationship. The horizontal axis is labeled x and 'Chores not completed,' with tick marks from 1 to 5. The vertical axis is labeled y and 'Amount earned,' with tick marks at 4, 8, 12, 16, and 20. A straight line with arrowheads at both ends slopes upward from left to right, passing through the origin (0 comma 0) and the point (1 comma 10), and extending beyond the top of the graph.

Image with description A line graph on a Cartesian coordinate plane showing a linear relationship. The horizontal axis is labeled 'Chores not completed,' with tick marks at intervals of 2 from 2 to 10. The vertical axis is labeled 'Amount earned,' with tick marks from 2 to 10 at intervals of 1. A straight line with arrowheads at both ends slopes downward from left to right, passing through the y-intercept at (0 comma 10) and the x-intercept at (10 comma 0).

Image with description A line graph on a Cartesian coordinate plane showing a linear relationship. The horizontal axis is labeled x and 'Chores not completed,' with tick marks from 1 to 5. The vertical axis is labeled y and 'Amount earned,' with tick marks at 2, 4, 6, 8, and 10. A straight line with arrowheads at both ends slopes downward from left to right, passing through the y-intercept at (0 comma 10) and the x-intercept at (1 comma 0).

Image with description A line graph on a Cartesian coordinate plane showing a linear relationship. The horizontal axis is labeled x and 'Chores not completed,' with tick marks at 2, 6, 10, 14, and 18. The vertical axis is labeled y and 'Amount earned,' with tick marks at 2, 6, 10, 14, and 18. A straight line with arrowheads at both ends slopes upward from left to right, passing through the y-intercept at (0 comma 10) and the point (10 comma 20).

Explanation

Samantha starts with $10, so she earns $10 when she completes all her chores (0 chores not completed). Each chore she misses reduces her allowance by $1, giving the rule amount earned = 10 − number of chores not completed. The graph should start at (0, 10) and slope downward; choice B shows this relationship, reaching $0 when 10 chores are missed.

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