# How do you find the slope and intercept of 4x = 3y + 6?

Feb 7, 2016

Slope: $\frac{4}{3}$
y-intercept: : $\left(- 2\right)$
x-intercept: $\frac{3}{2}$

#### Explanation:

A linear equation in standard form: $A x + B y = C$
has a slope of $\left(- \frac{A}{B}\right)$

Re-writing $4 x = 3 y + 6$ into standard form:
$\textcolor{w h i t e}{\text{XXX}} 4 x - 3 y = 6$
$\rightarrow$ slope $= - \frac{4}{- 3} = \frac{4}{3}$

The y-intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} 4 \times 0 = 3 y + 6$
$\rightarrow y = - 2$

The x-intercept is the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXX}} 4 x = 3 \times 0 + 6$
$\rightarrow x = \frac{6}{4} = \frac{3}{2}$