Forms of linear equations: summary

1. $y+2=\frac{4}{5}(x-2)$.

The line passes through $(-3,-6)$ and $(2,-2)$.

We don't have the $y$-intercept so it's most comfortable to write an equation in point-slope form.

$\begin{aligned} \text { Slope } &=\frac{(-2)-(-6)}{2-(-3)} \\ &=\frac{4}{5} \end{aligned}$

Using the point $(2,-2)$, an equation that represents the line is $y+2=\frac{4}{5}(x-2)$.

2. $y=\frac{3}{2} x+3$.

The line passes through $(0,3)$ and $(2,6)$.

We have the $y$-intercept so it's most comfortable to find the slope-intercept form of the line.

$\begin{aligned} \text { Slope } &=\frac{6-3}{2-0} \\ &=\frac{3}{2} \end{aligned}$

An equation that represents the line is $y=\frac{3}{2} x+3$.

3. $y-4=\frac{7}{5}(x+2)$.

The line passes through $(-7,-3)$ and $(-2,4)$.

We don't have the $y$-intercept so it's most comfortable to write an equation in point-slope form.

$\begin{aligned} \text { Slope } &=\frac{4-(-3)}{(-2)-(-7)} \\ &=\frac{7}{5} \end{aligned}$

Using the point $(-2,4)$, an equation that represents the line is $y-4=\frac{7}{5}(x+2)$.

4.  $y=\frac{6}{5} x-5$

The line passes through $(0,-5)$ and $(5,1)$.

We have the $y$-intercept so it's most comfortable to find the slope-intercept form of the line.

$\begin{aligned} \text { Slope } &=\frac{1-(-5)}{5-0} \\ &=\frac{6}{5} \end{aligned}$

An equation that represents the line is $y=\frac{6}{5} x-5$.