91Ó°ÊÓ

We are given two points i.e. $(-2,0)$and $(-3,-2)$.

We need to find the equation of the line containing these points in slope-intercept form.

• The slope-intercept form of a line having the slope $m$and the y-intercept $b$is $y=mx+b$
• When two points $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$of a line are given, the slope of the line is $m=\frac{y_2-y_1}{x_2-x_1}$
• The point-slope form of an equation of a line can be given as $y-y_1=m(x-x_1)$where$m$is the slope and$(x_1,y_1)$ is a point in the line.

The two points on the line are $(-2,0)$and $(-3,-2)$

Therefore the slope of the line is

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-0}{-3-(-2)} \\ m=\frac{-2}{-3+2} \\ ⇒m=\frac{-2}{-1} \\ ∴m=2 \end{gathered}$$

Thus the slope of the line containing the points $(-2,0)$and $(-3,-2)$is$2$.

Choose one point among the two points $(-2,0),(-3,-2)$

Let $\left(x_1,y_1\right)=\left(-2,0\right)$. We know that $m=2$

By the slope-point form we have,

role="math" localid="1644468843306" $$\begin{gathered} y-y_1=m(x-x_1) \\ y-0=2(x-(-2\left)\right) \\ y=2(x+2) \\ y=2x+4 \end{gathered}$$

Therefore, the slope-intercept form of the line containing the points$\left(-2,0\right)$and$(-3,-2)$is$y=2x+4$