Question

An athlete is running in a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete is from the school is given by y (in miles), where x + 10y = 260 (Note: 0 ≤ x ≤ 10 and 0 ≤ y ≤ 26). Complete the steps below to understand how to find the intercepts of the equation and what they represent.
Use the relationship between x and y to find the time it takes for the runner to reach the school.

Answer 1

Given x + 10y = 260 ; talso 0 ≤ x ≤ 10 and 0 ≤ y ≤ 26

to find the intercepts, set x=0

0 + 10(y-intercept) = 260

y-intercept = 26 miles at x=0; so runner is 26 miles from school at the start


then set y=0

x-intercept + 10(0) = 260

x-intercept = 260 minutes at y=0; so runner reaches school after 260 minutes

NOTE: the x-intercept is beyond the given range of 0 ≤ x ≤ 10; perhaps there is a typo n the range should 0 ≤ x ≤ 1000 instead?

Answer 2

Here, we have the limits:  0 ≤ x ≤ 10 and 0 ≤ y ≤ 26

When, x = 0, y = 260/10 = 26
x = 1, y = 250/10 = 25.9
x = 2, y = 258/10 = 25.8
x = 3, y = 257/10 = 25.7

and so on....for x = 10, y = 250/10 = 25

Intercepts would be: (0, 26), (1, 25.9) (2, 25.8) (3, 25.7), (4, 25.6), (5, 25.5) (6, 25.4) (7, 25.3) (8, 25.2), (9, 25.1), (10, 25)

x-coordinate represents the time taken by the athlete, and y represents the distance, he covered in that time.

Hope this helps!