Chapter 3, Problem 11STP

To determine

The direct variation equation to represent the given graph.

Answer to Problem 11STP

  $y=2x$

Explanation of Solution

Given:

The figures:

  

Concept Used:

Equation of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $y-y_1=m\left(x-x_1\right)$ , where $\text{slope, }m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Observe that the given line passes through the points $\left(0,0\right)\text{ and }\left(1,2\right)$ . So, the slope of the line passing through these points is

  $\begin{array}{c}\text{slope, }m=\frac{2-0}{1-0}\\ =\frac{2}{1}\\ =2\end{array}$

So, the equation of the line passing through the point $\left(0,0\right)$ and having slope $m=2$ is given by

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ y-0=2\left(x-0\right)\\ y=2x\end{array}$

Thus, direct variation equation that represents the given graph is $y=2x$ .