Chapter 0.1, Problem 23E

To determine

To write an equation for the line given in the graph.

Answer to Problem 23E

The equation of the line given in the graph:

  $y=2.5x$ .

Explanation of Solution

Given the graph of a line

  

Also, it is given that the line passes through the origin and the upper right point of the window.

Concept Used:

Equation of a line passing through two points:

The equation of a line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is as follows:

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot \left(x-x_1\right)$ .

Calculation:

It is given that the line passes through the origin $\left(0,0\right)$ .

Also, it is given that the line passes through the upper right point of the window.

That is, the line passes through the point $\left(10,25\right)$ also.

Thus, the line passes through the points $\left(x_1,y_1\right)=\left(0,0\right)$ and $\left(x_2,y_2\right)=\left(10,25\right)$ .

To find the equation of the line, substitute $\left(x_1,y_1\right)=\left(0,0\right)$ and $\left(x_2,y_2\right)=\left(10,25\right)$ in the equation $y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot \left(x-x_1\right)$ :

  $y-0=\frac{25-0}{10-0}\cdot \left(x-0\right)$ .

Simplify the equation $y-0=\frac{25-0}{10-0}\cdot \left(x-0\right)$ :

  $\begin{array}{c}y-0=\frac{25-0}{10-0}\cdot \left(x-0\right)\\ y=\frac{25}{10}\left(x\right)\\ y=2.5x\end{array}$ .

Thus, the equation of the line given in the graph:

  $y=2.5x$ .

Conclusion:

The equation of the line given in the graph:

  $y=2.5x$ .