Question

A local pizza shop charges a $2 delivery fee plus $1.50 per mile traveled. The equation y = 1.50x + 2 represents
the total cost (y) in dollars for a delivery that is x miles away. In this equation, the y-intercept represents ____.
2. A car rental company charges $30 per day plus $0.15 per mile driven. The equation y = 30x + 0.15m represents
the total cost (y) in dollars, where x is the number of days and m is the number of miles driven. Which of the
following statements is true about the graph of this equation?
A. It will be a straight
line in a
two-dimensional
coordinate plane
C. It will be a
three-dimensional
surface, as it involves
three variables
B. It will be a parabola
in a two-dimensional
coordinate plane
D. It cannot be
graphed because it
involves more than
two variables
3. A rectangle’s perimeter is 24 inches. Let x represent the length and y represent the width of the rectangle. Write
an equation that represents this situation, and explain how the graph of this equation in the coordinate plane
represents all possible dimensions of rectangles with a perimeter of 24 inches. Include in your explanation what
the intercepts of this graph represent in the context of the problem.

Answers

GPT-5 mini
1. In y = 1.50x + 2 the y-intercept is 2, which represents the $2 flat delivery fee (the cost when the distance x = 0).

2. C. Because y depends on two independent variables x and m, the graph is a surface in three-dimensional space (in fact a plane), so choice C is correct.

3. Perimeter 24: 2(x + y) = 24, so x + y = 12 (equivalently y = 12 − x).
This line in the coordinate plane gives all ordered pairs (x,y) whose sum is 12 — i.e., all possible length and width pairs that produce perimeter 24. Physically we restrict to x ≥ 0 and y ≥ 0 (more realistically x > 0 and y > 0), so the relevant portion is the segment of the line from (0,12) to (12,0). The intercepts: (0,12) means length 0 and width 12 (a degenerate rectangle), and (12,0) means length 12 and width 0.