Question

Written Portion

The graph below shows the relationship between time and distance traveled
by a race car moving at a constant rate and at its maximum speed. How long
did it take the race car to travel 480 miles?
Race Car Data
Distance (miles)
800
700
600
500
8400
300
200
100
0.5 1.5 2.5 3.5 4.5 5.5 6.5
Time (hours)

Answer 1

2.4 hours

Explanation:

The graph is a straight line graph. A straight line graph is used to represent a linear equation. A linear equation is represented by the equation: y = mx + c, where y is the dependent variable, x is the independent variable, m is the slope (rate of change) and c is the intercept.

A line passing through the point
`(x_1,y_1)\ and\ (x_2,y_2)\` can be represented by the equation:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)`

Let y represent the distance in miles and x represent the time in hours. From the graph, the line pass through (0.5, 100) and (3.5, 700). Hence using:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-100=(700-100)/(3.5-0.5) (x-0.5)\\\\y-100=200(x-0.5)\\\\y-100=200x-100\\\\y=200x-100+100\\\\y=200x\\\\To\ travel\ 480 \ miles,we\ substitute\ y=480\ and\ find\ x\\\\480=200x\\\\x=480/200\\\\x=2.4\ hours`