Question

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

Answer 1

`"slope " =2," y-intercept " =-1`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

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

Rearrange the given equation into this form.

add 4x to both sides.

`cancel(-4x)cancel(+4x)+2y=-2+4x`

`rArr2y=4x-2`

To obtain y as the subject, divide ALL terms on both sides by 2

`(cancel(2) y)/cancel(2)=4/2x-2/2`

`rArry=2x-1larr" in form y = mx + b"`

Extracting m and b gives.

`"slope " =m=2" and y-intercept " =b=-1`