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:

$\begin{gathered} y=-\frac{3}{5}x-4 \\ 3x+5y=2 \end{gathered}$

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:

$m=\frac{-A}{B}$

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:

$m=\frac{-A}{B}=\frac{-3}{5}$

As both slopes are equal, both lines are parallel.