Question

describing effects of a change in slope and y-intercept
the yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is ( y = \frac{1}{10}x + 60 ) for a member and ( y = \frac{1}{5}x ) for a nonmember. explain how the graph of a nonmember’s yearly cost will differ from the graph of a member’s yearly cost.
nonmember’s graph starts at (0,0) (no fixed fee), while member’s starts at (0,60)
sample response: the graph of a nonmember’s yearly cost will be steeper, but start lower than the graph of a member’s yearly cost.
what did you include in your response? check all that apply.
☐ the graph of a nonmember’s yearly cost is steeper
☐ the graph of a nonmember’s yearly cost has a lower y - intercept.
☐ the graph of a member’s yearly cost starts higher, but is less steep.

Explanation:

1. Slope comparison: The slope of the nonmember's cost function is $\frac{1}{5}$, and the member's is $\frac{1}{10}$. Since $\frac{1}{5} > \frac{1}{10}$, the nonmember's graph is steeper.
2. y-intercept comparison: The y-intercept of the nonmember's function is $0$ (starts at $(0,0)$), while the member's is $60$ (starts at $(0,60)$). So the nonmember's graph has a lower y-intercept, and the member's graph starts higher but is less steep.

All three statements correctly describe the differences between the two graphs.

Answer:

• The graph of a nonmember's yearly cost is steeper
• The graph of a nonmember's yearly cost has a lower y-intercept
• The graph of a member's yearly cost starts higher, but is less steep