Question

The graph shows the relationship between the distance Justin can drive his car and the amount of gas needed for the distance. How far can Justin drive with one gallon of gas?What’s the equation for the graph?

Answer 1

`\begin{gathered} 1)25 \\ 2)y=25x \end{gathered}`

1) In this question, we can see the graph of this proportional relationship between distance (y-axis) and gallons of gas (x-axis).

2) Thus, we can simply by inspection, examine the graph check the following corresponding output value:

Thus, we can see the point (1, 25) which 25 miles correspond to 1 gallon.

3) Let's pick another point to plug into the slope formula as well as that point (1,25) so we can choose the origin (0,0)

`m=(y_2-y_1)/(x_2-x_1)=(0-25)/(0-1)=(-25)/(-1)=25`

Note that the line passes through the origin, so the y-intercept is 0. Therefore we can write out the rule of this function as:

`y=25x`