Chapter 1.3, Problem 62E

To determine

An equation of the line passing through the pair of points $\left(-8,0.6\right),\left(2,-2.4\right)$ and its graph.

Answer to Problem 62E

The slope − intercept form of the equation of the given line is $y=\frac{-3}{10}x-\frac{18}{10}$

Explanation of Solution

Given information :

Given pair of points $\left(-8,0.6\right),\left(2,-2.4\right)$ .

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

  $\begin{array}{l}for(x_1,y_1)=\left(-8,0.6\right),(x_2,y_2)=\left(2,-2.4\right)\\ m=\frac{-2.4-0.6}{2+8}\\ =-\frac{3}{10}\\ \therefore m=-\frac{3}{10}\end{array}$

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 $m=-\frac{3}{10}$ and point $(x_1,y_1)=\left(-8,0.6\right)$ in above equation $(1)$ , we get

  $\begin{array}{l}\Rightarrow y-0.6=-\left(\frac{3}{10}\right)\left(x+8\right)\\ \Rightarrow 10y-6=-3x-24\\ \Rightarrow 10y=-3x-18\end{array}$

  $\therefore y=\frac{-3}{10}x-\frac{18}{10}$

Hence, slope − intercept form of the equation of the given line is $y=\frac{-3}{10}x-\frac{18}{10}$

Graph: The graph of $y=\frac{-3}{10}x-\frac{18}{10}$ is

  

Interpretation: Form above graph, we can observe that the graph of line passes through the given pair of points $\left(-8,0.6\right),\left(2,-2.4\right)$ .