prove lines are parallel

Question

prove -1/3x+2/3y=7 and 2x-4y=5 are parallel

Answer 1

The general rule is to put each of the sentences into slope-intercept form

 

Y = Ax + B

 

If they both come out with the same slope constant A and different intercept constants B, then they are parallel.  

 

In this case, though, I'd probably just be lazy and multiply the first equation by 6 on each side, which will give you an equation with the same coefficients for X and Y, but a different constant.  By definition, those lines will be parallel, since any combination of X and Y that meets the first one will fail the second one, so they share no points in common.

 

Given that I don't know your teacher, I'll tell you to do the slope-intercept method. that will certainly get you full credit.

 

 

Answer 2

Two lines are parallel if they have the same slope.  Put both equations into the slope-intercept form, y = mx + b, where m is the slope:

 

(-1/3)x + (2/3)y = 7

(2/3)y = (1/3)x + 7

y = (1/2)x + (21/2)

 

The slope is m = 1/2

 

2x - 4y = 5

-4y = -2x + 5

y = (2/4)x - 5/4

y = (1/2)x - 5/4

 

The slope is m = 1/2

 

Since the two lines have the same slope (m = 1/2), they are parallel.