The graph represents the cost of renting a car based on the distance traveled Distance Find the equation of the linear function that models the graph

Question

(0,20), (10,22.5) and (20,25)

Answer 1

To find the equation of the linear function that models the given points $(0,20)$, $(10,22.5)$, and $(20,25)$, we can start by calculating the slope of the line using two of the points.

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Let's use the points $(0,20)$ and $(10,22.5)$:

$$m=\frac{22.5-20}{10-0}=\frac{2.5}{10}=0.25$$

Now, we have the slope $m=0.25$. Next, we can use the point-slope form of the equation of a line, which is:

$$y-y_1=m(x-x_1)$$

Using the point $(0,20)$:

$$y-20=0.25(x-0)$$

Simplifying this, we get:

$$y-20=0.25x$$ $$y=0.25x+20$$

Now, we can confirm that this equation matches the remaining points. Let's check point $(10,22.5)$:

$$y=0.25(10)+20=2.5+20=22.5$$

And now check point $(20,25)$:

$$y=0.25(20)+20=5+20=25$$

Both points satisfy the equation.

Thus, the equation of the linear function that models the graph is:

$$y=0.25x+20$$