Writing Equations of Lines Practice

1. Complete the equation of the line through $(-1,6)$ and $(7,-2)$.

   Use exact numbers.

   $y=$ 

2. Complete the equation of the line through $(3,-1)$ and $(4,7)$.
   

   Use exact numbers.

   $y=$

3. Complete the equation of the line through $(-10,-7)$ and [(-5,-9)\).
   

   Use exact numbers.

   $y=$

4. Complete the equation of the line through $(4,-8)$ and $(8,5)$.
   

   Use exact numbers.

   $y=$
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/e/slope-intercept-equation-from-two-points
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1. 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 $y=-x +5$.

   ---

2. 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 $y=8x -25$.

   ---

3. 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 $y=-\dfrac{2}{5}x -11$.

   ---

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