To determine whether two lines are parallel, we need to look at the slopes of those lines. If they are the same, they are parallel.
We have two lines:
[tex]y= \frac{2}{3}x-17 [/tex]
[tex]4x-6y=-6[/tex]
In order to compare the slopes, let's rearrange the second equation to look like the first:
[tex]4x-6y=-6[/tex]
[tex]-6y=-4x-6[/tex]
[tex]y= \frac{-4}{-6}x+ \frac{-6}{-6} [/tex]
[tex]y= \frac{2}{3}x+1 [/tex]
So then let's compare these two equations again.
[tex]y= \frac{2}{3}x-17 [/tex]
[tex]y= \frac{2}{3}x+1 [/tex]
In slope-intercept form, y = mx +b, m is equal to the slope. In this case, both lines have the same slope, and therefore, they are parallel.
