# How do you find the slope and intercept of 8x + 4y = -96?

May 6, 2016

$m = - 2$ ,x-intercept=-12
y-intercept=-24

#### Explanation:

$8 x + 4 y = - 96$
Dividing both sides by 4 we have
$2 x + y = - 24$
$\implies y = - 2 x - 24$
Comparing this with slope imtercept form $y = m x + c$ .where m is the slope c is intercept from y-axis
Slope=-2 and y-intercept$c = - 24$

x-intercept can be had by putting y=0 in the equation

$0 = - 2 x - 24 \implies x = - 12$
So x-intercept=-12

May 6, 2016

Slope = $- 2$

$y$-intercept is $- 24$ and the point is $\left(0 , - 24\right)$

$x$-intercept is $- 12$ and the point is $\left(- 12 , 0\right)$

#### Explanation:

We can see that 4 is a factor common to all the terms in the given equation.

$4 \times 2 x + 4 y = - 24 \times 4$

$\implies 4 \left(2 x + y\right) = - 24 \times 4$

Divide both sides by 4:

$\frac{4 \left(2 x + y\right)}{4} = \frac{- 24 \times 4}{4}$

$\implies 2 x + y = - 24$

This can also be written as

$y = - 2 x - 24$

First, we will find the slope

The equation of a line is of the form $\textcolor{red}{y = m x + c}$

Where, $m$ is the slope of the line and $c$ is the $y$-intercept.

Comparing $y = m x + c$ to the given equation, $y = - 2 x - 24$

$m = - 2$ and $c = - 24$

$\implies$ Slope $= - 2$ and $y$-intercept $= - 24$

The $y$-intercept is the point where the line cuts the $y$-axis. i.e. the point when $x = 0$.

Therefore, the $y$-intercept is the point $\left(0 , - 24\right)$.

Next, we find the intercepts

We have already found the $y$-intercept above.

The $x$-intercept is the point where the line cuts the $x$-axis. i.e. to find the point when $y = 0$.

Pretty simple.

Here is a step-by-step to work out the $x$-intercept. The $x$-intercept is the point $\left(- 12 , 0\right)$.