Chapter 3, Problem 2PFA

To determine

To find: Equation represented by the graph.

Answer to Problem 2PFA

  $y=\frac{5x}{2}+5$

And

  $-5x+2y=10$

Explanation of Solution

From the given Graph we can say that the line passed through the points

  $\left(x_1,y_1\right)=\left(-2,0\right)$

  $\left(x_2,y_2\right)=\left(0,5\right)$

Using two-point formula

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

On substituting values

We get

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \Rightarrow y-0=\left(\frac{5-0}{0-\left(-2\right)}\right)\left(x-\left(-2\right)\right)\\ \Rightarrow y=\left(\frac{5}{0+2}\right)\left(x+2\right)\\ \Rightarrow y=\left(\frac{5}{2}\right)\left(x+2\right)\\ \Rightarrow y=\frac{5}{2}x+\frac{5}{2}\times 2\\ \Rightarrow y=\frac{5x}{2}+5\end{array}$

Therefore $y=\frac{5x}{2}+5$ represents the given graph

On rearranging terms of above equation

We get

  $\begin{array}{l}y=\frac{5x}{2}+5\\ \Rightarrow y=\frac{5x+\left(5\times 2\right)}{2}\\ \Rightarrow y=\frac{5x+10}{2}\\ \Rightarrow 2y=5x+10\\ \Rightarrow -5x+2y=10\end{array}$

Therefore

  $y=\frac{5x}{2}+5$ and $-5x+2y=10$ represents the given graph.