Question

You and your friend leave your houses at the same time to meet at a restaurant. the distance (in miles) your friend is from the restaurant is given by y=−40x+200y=−40x+200, where xx is the number of hours since your friend left home. you live 100 miles from the restaurant and arrive at the same time as your friend. write a linear equation that represents your distance from the restaurant.

Answer 1

When x=0 the friend is 200 miles from the restaurant and at x=5 the friend reaches the restaurant.
When x=0 you are 100 miles from the restaurant, so 100 is the y intercept, and when x=5 you reach the restaurant so 5 is the x intercept. We have y=mx+100 and y=0 when x=5, so 0=5m+100 therefore m=-20 and the equation is y=-20x+100.