How do you find the slope and y intercept of -12x+3y=-60?

Sep 29, 2015

Slope: $4$
y-intercept: $- 20$

Explanation:

Method 1
For a linear equation in standard form: $A x + B y = C$
$\textcolor{w h i t e}{\text{XXX}}$the slope is $m = - \frac{A}{B}$
In this case $A = - 12$ and $B = 3$
$\textcolor{w h i t e}{\text{XXX}}$so the slope is $m = - \frac{- 12}{3} = 4$

The y-intercept is the value of $y$ when $x = 0$
Replacing $x$ with $0$ in the original equation:
$\textcolor{w h i t e}{\text{XXX}} - 12 \left(0\right) + 3 y = - 60$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} 3 = - 20$

Method 2
Alternately, you could rearrange the expression into "slope-intercept form: $y = m x + b$
(with slope $= m$ and y-intercept $= b$)

Given
$\textcolor{w h i t e}{\text{XXX}} - 12 x + 3 y = - 160$
Add $12 x$ to both sides
$\textcolor{w h i t e}{\text{XXX}} 3 y = 12 x - 60$
Divide by $3$
$\textcolor{w h i t e}{\text{XXX}} y = 4 x - 20$
$\textcolor{w h i t e}{\text{XXXXX}} \left(= 4 x + \left(- 20\right)\right)$
which is "slope-intercept form"
with slope $m = 4$ and y-intercept$= - 20$