Question

Line a: y=6x-8 Line b: -9x-54y=7

Are these lines parallel or perpendicular?

Answer 1

line b can be rewritten in the form y=mx + b to match the form of line a

line a: y = 6x - 8

line b : y= 9x + 7/-54 = y = -1/6x -7/54

a line that is perpendicular to the original follows his formula:

m = -1/m where the slope of he perpendicular line is -1/m

our original slope was 6

slope of perpendicular line = -1/6

Because the slopes of these two lines follow "m = -1/m" the lines are perpendicular.

Answer 2

this*

Answer 3

m = -1/m means you take the slope of one line, then make it negative and take the reciprocal, that is he slope of your perpendicular line.

If the slopes appear to be negative reciprocals of one another, then the lines are perpendicular.

Answer 4

@Jhannybean I don't understand how to rewrite line b

Answer 5

ok, for line b, you have - 9x - 54y = 7

We want to isolate y on one side and put everything elseon the other, so that we could visualize it in the form y= mx+b

We can first isolate the "y" by adding + 9x to both sides

+9x - 9x -54y = +9x +7

Now the 9x's can cancel out on the left side

-54y = 9x +7

we have our y on one side and our x on the other, but now we want to have y all by itself, so we're going to have to divide the ENTIRE equation by - 54,because whatever we do to one side of the equation, we do to the right.

-54y / -54 = ( 9x + 7 ) /- 54

now we can cancel out the -54's from the left side.

y = ( 9x + 7)/ -54

now we divide each term in the numerator by -54

y = 9x/-54 + 7/-54

What is 9/-54? this can be reduced to -1/6 because 9 goes into 54 6 times.

We can now write the simplified version of his equation

y = -1/6 x - 7/54

Answer 6

@Jhannybean Thank you!

Answer 7

Do you understand how it works now? :)

Answer 8

@Jhannybean Yes :)