Question

Determine the slope of a line perpendicular to
the line with equation: 6x - 4y = 30. Show your work and/or explain how you did it. Medal will be rewarded for your patronage and accuracy & correctness of answer. Thanks! :DDD

Answer 1

do you know how to find the slope in the equation 6x - 4y = 30 ?

Answer 2

put the equation in y = mx + b form, and the slope of the line is in the m position. Once you find the slope, we will work on finding the slope of the perpendicular line.

Answer 3

Well I just switched the equation into slope-intercept form: y = mx + b

Answer 4

what did you get ?

Answer 5

y = -3/2 - 15/2

Answer 6

Solve for Y. The x coefficient will be the slope of the line.

-4y = -6x + 30 (subtract 6x from both sides)
y = 3/2x - 15/2 (Divide both sides by -4)
Slope is 3/2

Answer 7

6x - 4y = 30
-4y = -6x + 30
y = -6/-4y + 30/-4
y = 3/2 - 15/2

the slope of the equation you were given is 3/2

for a perpendicular line, you have to take the negative reciprocal of that slope. To do that, you " flip " the fraction and change the sign.
Therefore, the negative reciprocal of 3/2 = -2/3.

so the slope of the perpendicular line you are looking for is -2/3.

Do you understand ?

Answer 8

\[6x - 4y = 30 --> \frac{ -4y }{ -4 } = \frac{ 6x }{ -4 } -\frac{ 30 }{ 4 }\]

Answer 9

6x - 4y = 30 (subtract 6x from both sides)
6x - 6x - 4y = -6x + 30 (combine like terms)
-4y = -6x + 30
divide by -4 to get y by itself
y = (-6/-4)y + (30/-4)
y = 3/2y - 15/2

slope is 3/2

negative reciprocal of 3/2 = - 2/3 (your perpendicular slope)

Answer 10

oops...typo ...y = 3/2x - 15/2

Answer 11

or just change it into slope - intercept form: y = mx + b

Answer 12

yes...y = mx + b form would be y = 3/2x - 15/2
and 3/2 is the slope of this equation.

perpendicular slope would be negative reciprocal of 3/2, which is -2/3

Answer 13

I got -3/2 - 15/2

Answer 14

it is not -3/2...it is 3/2. I worked the problem out above....

Answer 15

It is, because -4y/4 = y; 6x/-4 = -3/2, 30/-4 = -15/2 or -7.5

Answer 16

let me show you again....
6x - 4y = 30
subtract 6x from both sides
6x - 6x - 4y = -6x + 30
leaving you with
-4y = -6x + 30
now we divide by -4
-4y/-4 = -6x/-4 + 30/-4
y = 3/2x - 15

you are messing up on dividing -6/-4, two negatives divided by each other = a positive.

Answer 17

understand ?

Answer 18

no, how about solving in by entering 6x - 4y = 30 into the slope intercept form: y = mx + b and solve it that way

Answer 19

that is what we just did....
y = 3/2x - 15 is slope intercept form.
and to find perpendicular slope, you take the negative reciprocal of slope 3/2 which is -2/3

Answer 20

no you didn't; I'll get you started: -4y = 6x + 30, go from there

Answer 21

no......
you have to subtract 6x from both sides to get -4y by itself.
therefore, it becomes -4y = -6x + 30

Answer 22

@RadEn ...can you explain this...he does not seem to understand me

Answer 23

It should be -15/4 not -15

Answer 24

@ybarrap ...can you explain this...he is not understand me

Answer 25

I understand it, you made an error -15 is wrong; it's -15/2

Answer 26

oops....-15/2.....however, that does not matter in this problem

Answer 27

we are just dealing with the slope, not the y intercept

Answer 28

I completely understand it, I just had to point that out

Answer 29

do you understand how the slope is 3/2 and not -3/2 ?

Answer 30

Great job guys!!

Answer 31

so the answer is -2/3, because the slope of the equation was 3/2x - 15/2

Answer 32

good deal :) yes...the perpendicular slopeis -2/3
Just remember, to find perpendicular, you take the negative reciprocal of the slope given

Answer 33

thanks ybarrap :)