An athlete is running in a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete i
s 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.
Given <span>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 </span>0 ≤ x ≤ 10; perhaps there is a typo n the range should <span>0 ≤ x ≤ 1000 instead?</span><span>
If we were to put this information into a slope-intercept form equation, the equation would be: y = 5x (dollars raised = 5 dollars per lap walked). In this case, we are going to use the variables l and d instead of x and y, respectively. The equation instead of being y = 5x, it is going to be d = 5l. In the slope-intercept form X will always be the independent variable and y the dependent variable, because the number we get for Y totally depends on what you plugged in for X. In this equation, l is the independent variable (the number of laps she walks) and d is the dependent variable (number of dollars).
It was used as the multiplier because the 5 represents the hours she's worked. If she uses the 1/5 graph she will find the unit rate of each time she gets paid an hour.
