Chapter 1.3, Problem 55E

To determine

An equation of the line passing through the pair of points $\left(5,-1\right),\left(-5,5\right)$ and its graph.

Answer to Problem 55E

The slope − intercept form of the equation of the given line is $y=\frac{-3}{5}x+2$

Explanation of Solution

Given information :

Given pair of points $\left(5,-1\right),\left(-5,5\right)$ .

Since slope $(m)$ of the line passing through the pair of points $(x_1,y_1),(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}for(x_1,y_1)=\left(5,-1\right),(x_2,y_2)=\left(-5,5\right)\\ m=\frac{5+1}{-5-5}\\ =-\frac{6}{10}\\ \therefore m=-\frac{3}{5}\end{array}$

As we know that the slope − intercept form of the equation of the line is $y-y_1=m\left(x-x_1\right)+c\mathrm{........}(1)$

Now substituting slope $m=-\frac{3}{5}$ and point $(x_1,y_1)=\left(5,-1\right)$ in above equation $(1)$ , we get $\begin{array}{l}\Rightarrow y+1=-\left(\frac{3}{5}\right)\left(x-5\right)\\ \Rightarrow 5y+5=-3x+15\\ \Rightarrow 5y=-3x+10\end{array}$

  $\therefore y=\frac{-3}{5}x+2$

Hence, slope − intercept form of the equation of the given line is $y=\frac{-3}{5}x+2$

Graph: The graph of $y=\frac{-3}{5}x+2$ is

  

Interpretation: Form above graph, we can observe that the graph of line passes through the given pair of points $\left(5,-1\right),\left(-5,5\right)$ .