Answer:
Yes, they are parallel.
Step-by-step explanation:
Parallel lines have the same slope. We must find the slopes of the two lines.
When the equation of a line is written in the slope-intercept form,
y = mx + b,
the slope is m.
The first line has equation
[tex] y = \dfrac{2}{3}x - 17 [/tex]
It is already written in the slope-intercept form. Comparing y = 2/3x - 17 with y = mx + b, you see that m = 2/3. The slope of the first line is 2/3.
Now we solve the second equation for y to obtain the slope-intercept form of that equation.
4x - 6y = -6
Subtract 4x from both sides.
-6y = -4x - 6
Divide both sides by -6.
[tex] \dfrac{-6}{-6}y = \dfrac{-4}{-6}x + \dfrac{-6}{-6} [/tex]
[tex] y = \dfrac{2}{3}x + 1 [/tex]
We now compare this form of the second equation with y = mx + b, and we see that m = 2/3.
Both equations have the same slope, 2/3, so the lines are parallel.
