Are the lines parallel?

Question

Are the graphs of the lines parallel? Exain. Y= 2/3x -17 and 4x -6y = -6

Answer 1

Dawn, you probably know this from Algebra 1.

You want to find the slope of each line. If they are equal, the lines are parallel (or even collinear!). If the slopes are different, they are not parallel.

The first line is already in slope-intercept form:

y = (2/3)x - 17

The second line needs to solved for y, and then you will know its slope as well.

Answer 2

Two lines with the same slope are parallel (or collinear).

Now. once and forever solve the Standard Form of a linear equation (Ax+By=C) for y (which produces the slope-intercept form [that is, y = mx + b, where m is the slope] of the equation) and remember that the slope, m, is -A/B. The slope of the equation 4x-6y=-6 is -4/(-6) = 2/3.

They are parallel lines.

Answer 3

Yes, the lines are parallel because the slopes of both lines are the same.

y₁=(2/3)x-17 where the slope of equation one is m₁=2/3

and

4x-6y₂=-6 => 6y₂=4x+6 => y₂=(2/3)+1 where the slope of equation 2 is m₂=2/3

As long as both slopes are equal, the lines are parallel.

Answer 4

The first equation is:

y = (2/3)x - 17

The 2nd equation can be solved for y:

-6y = -4x - 6

y = (2/3)x + 1

The slope-intercept form for a line is y = mx + b (m=slope, b=y-intercept)

Parallel lines will have equal slopes, if they are not equal, the lines are NOT parallel.

Perpendicular lines will have slopes that are related by m₂ = -1/m₁

Here, the slopes are equal (2/3), so the two lines are parallel.

Answer 5

Lines are parallel if they have the same slopes. You can find the slope by looking at the value attached to the "x" when the equation is in y=ax+b form.

y=2/3x-17: slope is 2/3

We need to rearrange the second equation.

4x-6y=-6

-6y=-4x-6

y=4/6x+1

y=2/3x+1: slope is 2/3

Both lines have slopes of 2/3, so the lines are parallel.