Question

HELP PLEASE FOR FAN + MEDAL!!!

–2x + 4y > 8

Write the equation in point-slope form for the line that is perpendicular to this line and contains the point (1, -4).

Answer 1

\(\normalsize\color{royalblue}{ \rm -2x + 4y > 8 }\)

Say it is: \(\normalsize\color{royalblue}{ \rm -2x + 4y = 8 }\)
and then please re-write it in a slope intercept form.

Answer 2

Slope intercept form is: \(\normalsize\color{royalblue}{ \rm y=mx+b }\)

Answer 3

Do this for me now, (but it won't be the final answer... beware of that)

Answer 4

8= -2x+4y is that it @SolomonZelman?

Answer 5

not really.

Answer 6

lets do it together:

Answer 7

\(\normalsize\color{royalblue}{ \rm -2x + 4y = 8 }\)
\(\normalsize\color{red}{ \rm +2x~~~~~~~~~~~+2x }\)

Answer 8

what do you then get?

Answer 9

0 and...10x i think

Answer 10

no,

Answer 11

8 and 2x are not like terms.
And on the left side, you left out 4y

Answer 12

it's 4?

Answer 13

what is 4?

Answer 14

the left side of the equation -2x + 2 and 4y

Answer 15

\(\normalsize\color{royalblue}{ \rm -2x+4y=8 }\)
\(\normalsize\color{royalblue}{ \rm -2x+4y\color{red}{+2x}=8\color{red}{+2x} }\)
\(\normalsize\color{royalblue}{ \rm \cancel{-2x}+4y\color{red}{\cancel{+2x}}=8\color{red}{+2x} }\)
\(\normalsize\color{royalblue}{ \rm 4y=8+2x }\)

Answer 16

then divide each term in the equation by 4....

Answer 17

\[y=\frac{ x }{ 2 }+8\]
That's what I got is that the equation in slope intercept form @SolomonZelman?

Answer 18

oh wait.

Answer 19

you forgot to divide the 8

Answer 20

\(\large\color{royalblue}{ \displaystyle y=\frac{x}{2}+2 }\)

Answer 21

oh right hold on let me do it again.

Answer 22

(I divided the 8 too)

Answer 23

I will re-write this, as: \(\large\color{royalblue}{ \displaystyle y=\frac{1}{2}x+2 }\)

Answer 24

and you need the line that is perpendicular to I will re-write this, as: \(\large\color{royalblue}{ \displaystyle y=\frac{1}{2}x+2 }\)

Answer 25

So, for a line with a slope m, a perpendicular line will have a slope of -1/m.

Answer 26

now, if your m is 1/2, then -1/m will be?

Answer 27

-0.5?

Answer 28

\(\large\color{royalblue}{ \displaystyle -\frac{1}{\frac{1}{2}} }\)

Answer 29

no, you are incorrect-:(`

Answer 30

hmmm okay hold on

Answer 31

how do i figure tht out?

Answer 32

\(\large\color{royalblue}{ \displaystyle -\frac{1}{\frac{1}{2}}=-1\div\frac{1}{2}=-1\times 2=?}\)

Answer 33

-2

Answer 34

yes.

Answer 35

now, you know that
\(\large\color{slate}{ y=2x+b }\)
but you need a y-intercept to make the line go through a point (1-4)

Answer 36

I mean point (1,-4) (I left out a comma)

Answer 37

plug in your point and solve for b

Answer 38

wait i plug in the points 1and -4 into x?

Answer 39

\(\large\color{slate}{ (-4)=2(1)+b }\) b=?

Answer 40

b=-6?

Answer 41

yes.

Answer 42

So, you have:
\(\large\color{slate}{ y=2x-6 }\)

Answer 43

donne

Answer 44

Thank you so much @SolomonZelman

Answer 45

yw