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

Answer:

$y=\frac{1}{2}x+\frac{3}{2}$

Step-by-step 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

$y=\frac{1}{2} x+2$

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 $\frac{1}{2}$.

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.

$y=\frac{1}{2}x +b$

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.

$-1=\frac{1}{2} (-5)+b\\-1=\frac{-5}{2}+b\\\frac{3}{2} =b$

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).

$y=\frac{1}{2}x+\frac{3}{2}$