Question

For which value of a are the graphs of –4 = 3x + 6y and ax – 8y = 12 parallel?
A a = –4
B a = -1/2
C a = 1/4
D a = 2

Answer 1

you want the slopes of both lines to be the same

Answer 2

so find the slopes of both lines and set them equal and solve for a

Answer 3

i got -4? is that correct

Answer 4

I think so
let's find out:
\[-4=3x+6y \\ \implies -3x-4=6y \\ y=\frac{-3x}{6}-\frac{4}{6} \\ y=\frac{-1}{2}x-\frac{2}{3} \]

\[ax-8y=12 \\ -8y=-ax+12 \\ y=\frac{-a}{-8}x+\frac{12}{-8} \\ y=\frac{a}{8}x+\frac{-3}{2}\]

this implies that -1/2 =a/8 since the lines are parallel
so yep a=-4

Answer 5

i had it like that but my 4 came out as a +4

Answer 6

well should be -4
since -1/2 is the same as -4/8
-1/2 is not the same as 4/8

Answer 7

\[\frac{-1}{2}=\frac{a}{8} \\ \text{ cross multiply } \\ -1(8)=a(2) \\ -8=2a \\ \text{ divide both sides by } 2 \\ \frac{-8}{2}=\frac{2a}{2} \\ \frac{-8}{2}=a \\ a=\frac{-8}{2} \\ a=-4\]

Answer 8

alot of work

Answer 9

you don't have to do all that work if you know that -1/2=-4/8

Answer 10

oh ok i use this in other problems still

Answer 11

i'll use

Answer 12

there is another way you could have looked at it...

Answer 13

\[\frac{-1}{2}=\frac{a}{8}\]
you could have said what number times 2 gives me 8

Answer 14

and you would well miss that would 4
since 2*4=8
since you multiply the bottom number by 4
you multiply the top number by 4

Answer 15

\[\frac{-1}{2}=\frac{a}{8} \\ \frac{-1}{2} \cdot \frac{4}{4}=\frac{-4}{8}=\frac{a}{8} \implies a=-4\]

Answer 16

there is another way to think about this one
and this is an easy fraction
like 1 is half of 2
and what number is half of 8?

Answer 17

1 is half of 2
4 is half of 8

and just don't forget to involve that negative back in

Answer 18

but anyways do you have any questions?

Answer 19

umm could u help me with this problem

Answer 20

What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?

Answer 21

ok let's first determine the slope of this line

Answer 22

to do this we need to find the slope of 2x+3y=-5

Answer 23

We need to do this because we know that perpendicular lines have opposite reciprocal slopes

Answer 24

so if we find the slope of 2x+3y=-5
and say it is a
then the slope of the line we are trying to find will be -1/a

Answer 25

anyways
do you know how to write 2x+3y=-5 in slope-intercept form?

Answer 26

i'll try

Answer 27

i got 3y+2x=-5

Answer 28

slope-intercept form is y=mx+b

Answer 29

So looking at 3y+2x=-5
we are not there yet

Answer 30

we need to solve the equation for y

Answer 31

First step: Try subtracting 2x on both sides.

Answer 32

ok

Answer 33

Let me see what you have after that step or if you were able to go further and solve for y by yourself let me see that equation pleaese

Answer 34

ok im still working on the bottom part

Answer 35

i keep getting 7/3 i dont know how

Answer 36

So you know I'm asking you to solve
3y+2x=-5 for y right?
First step was to subtract 2x on both sides:
This gives you 3y=-2x-5
You need to do one more step to isolate y. Do you know what it is?

Answer 37

subtract the 3

Answer 38

no

Answer 39

to undo multiplication you divide

Answer 40

3y is 3 times y

Answer 41

you need to divide both sides by 3

Answer 42

oh

Answer 43

\[3y=-2x-5 \\ \frac{3y}{3}=\frac{-2x-5}{3} \\ \\ y=\frac{-2x}{3}-\frac{5}{3} \\ y=\frac{-2}{3}x-\frac{5}{3}\]
so what is the slope of this line?

Answer 44

The slope of y=mx+b is m
The slope of y=-2/3*x-5/3 is?

Answer 45

umm