Parallel Lines

Question

The admission cost to enter a fair is $5. The cost to ride each ride at the fair is $1.50. Julie received a ½-off coupon that applies to the admission price. Julie decides to graph the total cost on the y-axis and the number of rides on the x-axis, using the equation to represent the total cost, and the equation to represent the discounted cost. Which best describes the appearance of the discounted cost line to that of the regular cost line?

A. less steep
B. more steep
C. same steepness, discounted cost line closer to the origin
D. same steepness, discounted cost line farther away from the origin

Answer 1

The total money she spends is equal to: 

 

cost to enter + 1.5 * number of rides she goes on

 

Let x = number of rides she goes on

Let y = cost

 

Then, originally, 

y=5+1.5x

 

Using her coupon, she will now spend 2.5 on admission, but the ride cost remains the same.  Then:

 

y=2.5 + 1.5x

 

These two lines have the same slope so the slope remains the same.  However, the y intercept value has been reduced from 5 to 2.5, so the grph is closer to the originl

 

Hence the solution is option C