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 \(y=\frac{6}{5} x-5\).