Writing Equations of Lines Practice

Let's find the slope:

$\begin{aligned}\text{Slope}&=\dfrac{-2-6}{7-(-1)}\\\\&=\dfrac{-8}{8}\\\\&=-1\end{aligned}$

The equation is $y=-1x+b$ for some $b$.

Let's plug the point $( {7}, {-2})$ to find $b$:

$\begin{aligned} y&=-1 x+b\\\\ {-2}&=-1( {7})+b\\\\-2&=-7+b\\\\5&=b\end{aligned}$

The equation is $y=-x +5$.

Let's find the slope:

$\begin{aligned}\text{Slope}&=\dfrac{7-(-1)}{4-3}\\\\&=\dfrac{8}{1}\\\\&=8\end{aligned}$

The equation is $y=8x+b$ for some $b$.

Let's plug the point $( {4}, {7})$ to find $b$:

$\begin{aligned} y&=8 x+b\\\\ {7}&=8( {4})+b\\\\7&=32+b\\\\-25&=b\end{aligned}$

The equation is $y=8x -25$.

Let's find the slope:

$\begin{aligned}\text{Slope}&=\dfrac{-9-(-7)}{-5-(-10)}\\\\&=\dfrac{-2}{5}\\\\&=-\dfrac{2}{5}\end{aligned}$

The equation is $y=-\dfrac{2}{5}x+b$ for some $b$.

Let's plug the point $( {-5}, {-9})$ to find $b$:

$\begin{aligned} y&=-\dfrac{2}{5} x+b\\\\ {-9}&=-\dfrac{2}{5}( {-5})+b\\\\-9&=2+b\\\\-11&=b\end{aligned}$

The equation is $y=-\dfrac{2}{5}x -11$.

Let's find the slope:

$\begin{aligned}\text{Slope}&=\dfrac{5-(-8)}{8-4}\\\\&=\dfrac{13}{4}\end{aligned}$

The equation is $y=\dfrac{13}{4}x+b$ for some $b$.

Let's plug the point $( {8}, {5})$ to find $b$:

$\begin{aligned} y&=\dfrac{13}{4} x+b\\\\ {5}&=\dfrac{13}{4}( {8})+b\\\\5&=26+b\\\\-21&=b\end{aligned}$

The equation is $y=\dfrac{13}{4}x -21$.