Question

Are the graphs of the lines in the graph parallel? y = 2/3x - 17 4x-6y= -6

Answer 1

You have put both in slope intercept form;;;;

y=2/3x-17 (already in slope-intercept form)

4x-6y=-6 (standard form)

For this, add 6y to both sides, and add 6 to both sides giving you...

6y=4x-6
Divide by 6 on both sides...

y=2/3x-1

Since both equations have the same slope, the graphs will be parallel.

Answer 2

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:
$y= \frac{2}{3}x-17$
$4x-6y=-6$

In order to compare the slopes, let's rearrange the second equation to look like the first:

$4x-6y=-6$
$-6y=-4x-6$
$y= \frac{-4}{-6}x+ \frac{-6}{-6}$
$y= \frac{2}{3}x+1$

So then let's compare these two equations again.

$y= \frac{2}{3}x-17$
$y= \frac{2}{3}x+1$

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.