Question

The graph shows a trip taken by a car, where t is the time (in hours) and y is the distance

(in miles) from Phoenix.


a. Find the y-intercept of the graph. What does it represent?
b. Find the slope of the graph. What does it represent? c. How long did the trip last? d. How far from Phoenix was the car at the end of the trip?
e. Write an equation that represents the graph

Answer 1

The answer is below

Explanation:

The equation of a graph of a linear function is in the form:

y = mx + b;

where m is the slope of the graph, b is the y intercept, y and x are the variable.

Since y represent distance on y axis and t represent time on the x axis. We see that the graph passes the points:

(0, 100) and (6, 400). The equation of the graph is:

`y-y_1=(y_2-y_1)/(t_2-t_1)(t-t_1) \\\\y-100=(400-100)/(6-0)(t-0)\\\\y-100= 50t\\\\y=50t+100`

a) The y intercept is 0. This means that initially the car is at 100 miles from Phoenix before the trip started. i.e. at 0 hours the distance is 100 miles.

b) The slope of the graph is 50. It means that the car traveled at a speed of 50 miles per hour

c) The end point of the graph is (6, 400), meaning the trip lasted 6 hours

d) The end point of the graph is (6, 400), meaning at the end of the trip, the car was 400 miles from Phoenix.