Question

name
find the slope, y-intercept of the line, and then write an equation in slope-intercept form. period
1)
points: (2,4), (5,0)
$m$: ______
$b$: ______
equation: ______
2)
points: (-3,-1), (-2,-4)
$m$: ______
$b$: ______
equation: ______

Explanation:

Step1: Calculate slope for Line 1

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(x_1,y_1)=(2,4)$, $(x_2,y_2)=(5,0)$
$m=\frac{0-4}{5-2}=\frac{-4}{3}$

Step2: Find y-intercept for Line1

Substitute $m=\frac{-4}{3}$, $(x,y)=(5,0)$ into $y=mx+b$
$0=\frac{-4}{3}(5)+b \implies b=\frac{20}{3}$

Step3: Write Line1 equation

Substitute $m$ and $b$ into slope-intercept form
$y=\frac{-4}{3}x+\frac{20}{3}$

Step4: Calculate slope for Line2

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(x_1,y_1)=(-3,-1)$, $(x_2,y_2)=(-2,-4)$
$m=\frac{-4-(-1)}{-2-(-3)}=\frac{-3}{1}=-3$

Step5: Find y-intercept for Line2

Substitute $m=-3$, $(x,y)=(-3,-1)$ into $y=mx+b$
$-1=-3(-3)+b \implies -1=9+b \implies b=-10$

Step6: Write Line2 equation

Substitute $m$ and $b$ into slope-intercept form
$y=-3x-10$

Answer:

For Line 1:

Slope $m$: $\boldsymbol{\frac{-4}{3}}$
y-intercept $b$: $\boldsymbol{\frac{20}{3}}$
Equation: $\boldsymbol{y=\frac{-4}{3}x+\frac{20}{3}}$

For Line 2:

Slope $m$: $\boldsymbol{-3}$
y-intercept $b$: $\boldsymbol{-10}$
Equation: $\boldsymbol{y=-3x-10}$