Question

Question3Use slopes and y-intercepts to determine if the lines y = - 3/5x -4 and 3x + 5y = 2 are parallel.Select the correct answer below:parallelnot parallel

Answer 1

Ok, so

We want to determine if the lines:

`\begin{gathered} y=-(3)/(5)x-4 \\ 3x+5y=2 \end{gathered}`

Are parallel.

Remember that a line is parallel to other one if their slopes are the same.

So, we're going to check each slope.

First, a line can be identified with two forms.

The first one, is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

The second one, is:

`Ax+By+C=0`

Where the slope can be found using the fact that it is:

`m=(-A)/(B)`

If we replace our values, the slope of the first line ( y = -3/5x - 4 ) is -3/5.

The second line:

`3x+5y-2=0`

Has a slope equal to:

`m=(-A)/(B)=(-3)/(5)`

As both slopes are equal, both lines are parallel.