Answer:
2.4 hours
Step-by-step 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
can be represented by the equation:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29)
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=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{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](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-100%3D%5Cfrac%7B700-100%7D%7B3.5-0.5%7D%20%28x-0.5%29%5C%5C%5C%5Cy-100%3D200%28x-0.5%29%5C%5C%5C%5Cy-100%3D200x-100%5C%5C%5C%5Cy%3D200x-100%2B100%5C%5C%5C%5Cy%3D200x%5C%5C%5C%5CTo%5C%20travel%5C%20480%20%5C%20miles%2Cwe%5C%20substitute%5C%20y%3D480%5C%20and%5C%20find%5C%20x%5C%5C%5C%5C480%3D200x%5C%5C%5C%5Cx%3D480%2F200%5C%5C%5C%5Cx%3D2.4%5C%20hours)