Question

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

Answer 1

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

Explanation:

`8x+4y=-96`
Dividing both sides by 4 we have
`2x+y=-24`
`=>y=-2x-24`
Comparing this with slope imtercept form `y=mx+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=-2x-24=>x=-12`
So x-intercept=-12

Answer 2

Slope = `-2`

`y`-intercept is `-24` and the point is `(0,-24)`

`x`-intercept is `-12` and the point is `(-12,0)`

Explanation:

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

`4xx2x + 4y = -24 xx 4`

`=> 4(2x+y) = -24 xx 4`

Divide both sides by 4:

`[4(2x+y)]/4 = (-24 xx 4)/4`

`=> 2x+y = -24`

This can also be written as

`y = -2x-24`

First, we will find the slope

The equation of a line is of the form `color(red)(y=mx+c)`

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

Comparing `y=mx+c` to the given equation, `y = -2x-24`

`m=-2` and `c=-24`

`=>` 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 `(0,-24)`.

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 `(-12,0)`.