parallel or perpendicular 6x + 7y = 1 and 7x - 6y = 7?

Answer 1

I want you to take a mantra from now on, regarding lines. When thinking parallel, always think, "same slope". When thinking perpendicular, always think, "negative reciprocal".

Your first step is to put both of those lines into slope-intercept form. This is accomplished by isolating y.

6x + 7y = 1
7y = -6x + 1
y = -6/7 x + 1/7

slope = -6/7, y-intercept is 1/7

7x - 6y = 7
-6y = -7x + 7
y = 7/6 x - 7/6

slope = 7/6, y-intercept is -7/6

Recall that parallel means "same slope". In this case, they aren't the same slope, because -6/7 (the first slope) isn't equal to 7/6 (the second slope).

Recall that perpendicular slope means "negative reciprocal". In this case, let's check what the negative reciprocal of the first slope is. I'll call the first slope m[1] and the second slope m[2]

m[1] = -6/7
Reciprocal means to flip the fraction, and negative means to multiply it by -1. So let's see what we get:

(-7/6)(-1) = 7/6, which is equal to m[2], our second slope! That means these two lines ARE indeed perpendicular!

Answer 2

Rearrange each equation into the form y=mx+b. M is the slope.

in this case,
a) y = -6/7 x + 1/7
b) y = 7/6 x + 1

If the slopes are the same then the lines are parallel. If the slopes are the negative inverses (i.e. -1/M) then they are perpendicular.

Answer 3

Alter them to be in the form of y = mx + c

7y = 1 - 6x
so,
y = -6/7 x + 1

6y = 7x - 7
y = 7/6 x - 7/6

since -6/7 is not equals to 7/6, they are parallel.
and since -6/7 * 7/6 = -1, they are perpendicular.

Hope this helps=)

Answer 4

these eq. r perpendicular as if these r in form y=mx+c,here m of 1st eq. is -7/6 n for second one is 6/7 n m1*m2=-1 that is the condition for perpendicular eq.,which is true here,hence these r perpendicular

Answer 5

perpendicular since the slope is equal to -1.

Answer 6

perpendicular
since the product of slope is -1.

Answer 7

perpendicular. 'coz the slopes are conjugated

Answer 8

perpendicular

Answer 9

perpendicular