Writing Slope-Intercept Equations

1.$y=-3 x+7$

Let's find the slope:

$\begin{aligned} \text { Slope } &=\frac{(-8)-1}{5-2} \\ &=\frac{-9}{3} \\ &=-3 \end{aligned}$

The equation is $y=-3 x+b$ for some $b$.

Let's plug the point $(2,1)$ to find $b$:

$\begin{aligned} &y=-3 x+b \\ &1=-3(2)+b \\ &1=-6+b \\ &7=b \end{aligned}$

The equation is $y=-3 x+7$.

2. $y=\frac{4}{3} x-12$

Let's find the slope:

$\begin{aligned} \text { Slope } &=\frac{-4-(-8)}{6-3} \\ &=\frac{4}{3} \end{aligned}$

The equation is $y=\frac{4}{3} x+b$ for some $b$.

Let's plug the point $(6,−4)$to find $b$:

$\begin{aligned} y &=\frac{4}{3} x+b \\ -4 &=\frac{4}{3}(6)+b \\ -4 &=8+b \\ -12 &=b \end{aligned}$

The equation is $y=\frac{4}{3} x-12$.

3. $y=8 x-25$.

Let's find the slope:

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

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

4. $y=-\frac{2}{5} x-11$

Let's find the slope:

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

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

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

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

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