Question

Are the graphs of the lines in the pair parallel? Explain. y = 2/3x – 17 4x – 6y = –6

Answer 1

They are parallel, because their slopes are the same.

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Since 4x does not contain the variable to solve for, move it to the right side of the equation by subtracting 4x from both sides.

−6y=−4x+6Multiply each term by −1/6 and simplify.
The equation will become:
y=2/3x-1
so yes. The lines are parallel to each other.

Answer 2

The condition for lines to parallel is that they must have the same slope.

y = (2/3)x - 17, by comparing to y = mx + c, slope m = (2/3).

4x - 6y = -6

-6y = -4x - 6 multiply through by -1

6y = 4x + 6

y = (4/6)x + 6/6

y = (2/3)x + 1 comparing to y = mx + c, slope m = 2/3.

So the slopes for the two lines are equal, so the pair of lines are parallel.