Question

How do you find the slope and y-intercept of the graph of 2x + 4y=-8?

Answer 1

slope `=-1/2`
y-intercept = - 2

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b can be extracted 'easily'.

Rearrange `2x+4y=-8" into this form"`

subtract 2x from both sides of the equation.

`rArrcancel(2x)-cancel(2x)+4y=-8-2xrArr4y=-2x-8`

now divide both sides by 4 to obtain y.

`rArr(cancel(4)^1 y)/cancel(4)^1=(cancel(-2)^-1)/cancel(4)^2 x-cancel(8)^2/cancel(4)^1`

`rArry=-1/2x-2" is equation in y = mx + b form"`

from this `"slope" =-1/2" and y-intercept" =-2`