Question

Find the equation of a line, in slope-intercept form of a line that passes through the point (-5, -1) and is parallel to -2x+4y=8. ​

Answer 1

`y=(1)/(2)x+(3)/(2)`

Explanation:

Let's write
`-2x+4y=8` to slope-intercept form.

We do this by solving for
`y`

`-2x+4y=8\\`

Add 2x to both sides

`4y=8+2x`

Divide both sides by 4

`y=(1)/(2) x+2`

Now that we have that equation in slope-intercept form, the question wants us to find a line that is parallel to it that passes the point (-5, -1).

A line is parallel to another line is they have the same exact slope.

The slope is
`(1)/(2)`.

Slope-intercept form:
`y=mx+b`, where
`m` is the slope and
`b` is the y-intercept.

So, let's see what we have here so far.

`y=(1)/(2)x +b`

All we have to do is find
`b`.

The question wants the line to pass the point (-5, -1).

Let's plug that point in.

`-1=(1)/(2) (-5)+b\\-1=(-5)/(2)+b\\(3)/(2) =b\\`

We have all the information needed to finish this problem!

So, the line that is parallel to
`-2x+4y=8` and passes through the point (-5, -1).

`y=(1)/(2)x+(3)/(2)`