# How do you calculate the slope, x intercept, and y intercept of the following equation: 3x + 4y= 0?

Jul 15, 2015

Slope = -3/4
The x intercept is 0
The y intercept is 0

#### Explanation:

Method 1 : Convert to slope intercept form
$\textcolor{w h i t e}{\text{XXXX}}$A linear equation in the form:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$y = m x + b$
$\textcolor{w h i t e}{\text{XXXX}}$is in slope intercept form with slope $= m$
$\textcolor{w h i t e}{\text{XXXX}}$and y-intercept $= b$
$3 x + 4 y = 0$

$\rightarrow 4 y = - 3 x + 0$

$\rightarrow y = - \frac{3}{4} x + 0$$\textcolor{w h i t e}{\text{XXXX}}$(slope intercept form with slope $- \frac{3}{4}$ and y intercept $= 0$
Substituting $y = 0$ into the original equation gives $x = 0$, the x-intercept.

Method 2: Use the slope formula for a standard form linear equation
$\textcolor{w h i t e}{\text{XXXX}}$A linear equation in standard form:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$
$\textcolor{w h i t e}{\text{XXXX}}$has a slope of $- \left(\frac{A}{B}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$or, in this case
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$-3/4#

The y-intercept is the value of y when $x = 0$
$\rightarrow$ y intercept $= 0$

The x-intercept is the value of x when $y = 0$
$\rightarrow$ x intercept $= 0$