Chapter 4, Problem 12SGR

To determine

To find the equation of line in slope-intercept form.

Answer to Problem 12SGR

  $y=\frac{2}{5}x+\frac{1}{5}$

Explanation of Solution

Given:

Line passing through the point $\left(-3,-1\right)$ with slope $\frac{2}{5}$ .

Concept used:

Equation of a line passing through the point $\left(x_1,y_1\right)$ with slope m is $y-y_1=m\left(x-x_1\right)$ .

Calculation:

Given,

  $m=\frac{2}{5},\left(x_1,y_1\right)=\left(-3,-1\right)$

Now the equation of the line is,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \Rightarrow y-\left(-1\right)=\frac{2}{5}\left(x-\left(-3\right)\right)\\ \Rightarrow y+1=\frac{2}{5}\left(x+3\right)\\ \Rightarrow y+1=\frac{2}{5}x+\frac{6}{5}\\ \Rightarrow y=\frac{2}{5}x+\frac{1}{5}\end{array}$