Question

Input the equation of the given line in standard form.

The line through (1, -4) and parallel to 2x + 3y = 4.

Answer 1

They have the same slope if they're parallel.

Write the given equation in the form
y = mx + b
m is the sope of both equations.

To find b you insert the given point an solve for b.

Answer 2

@Lyrae How would you write it out into an equation?

Answer 3

By putting the equation 2x + 3y = 4 into slope intercept form, it'll be easier for us to indicate what the slope of that equation is.

We know that parallel lines have the same slope, but (possibly) different y-intercepts.

2x + 3y = 4 \(\ \implies\) 3y = -2x + 4 \(\ \implies\) y = (-2/3)x + 4\3

We know that in slope intercept form, our equation is y = mx + b where m is the slope.
In this case, our m = (-2/3)

Answer 4

the new equation is also in the form y = mx + b, so you'll have to calculate m and b from what they given you.

Answer 5

now that we have our slope, m = -2/3 and our point, ( 1, -4) , we can use point-slope form.

\(\ y- y_0 = m(x-x_0)\)

Our point, (1,-4) corresponds to \(\ (x_0, y_0)\)

Answer 6

plugging in the values m, and our points, we can rewrite our equation as \(\ (y - (-4)) = (-\frac{2}{3}) (x-1)\)

Can you simplify this? :D

Answer 7

y-4=-2/3x-2/3?

Answer 8

thats simplified.

Answer 9

When you multiply a (-1) to a constant that is already -ve, it becomes +

Answer 10

yeah. thats what I done with the (-4)

Answer 11

Ahh, then you must have meant y+4?

Answer 12

no cause there is already a subtraction. y-(-4)... so shouldn't the -4 be a positive.... so the y- would remain the same. it would be y-4 instead of y--4

Answer 13

No no.

Let's say, for example we have 5- (-7). You could rewrite this as 5 + 7.

Answer 14

okay. I getcha!

Answer 15

Also, another way to think about it, even though it's a little obscure, is 5 + [-1(-7)] How would you simplify this?

Answer 16

-1(-7)=7... then 5+7=12

Answer 17

Yes! Good job.

Answer 18

Therefore, y- (-4) works the same way :D

you could think of it the same way, y - [-1(-4)] = y+4

Answer 19

okay (:

Answer 20

:3

so we have y + 4 = (-2/3)x -2/3 :)

Answer 21

Now all we have to do is subtract -4 to both sides of the equation, and we'll have our answer in slope-intercept form!

Answer 22

Don't you take the 4 to the -2/3? like -2/3 -4=-4 2/3?

Answer 23

what would be the common denominator?

Answer 24

multiply them?

Answer 25

the 3 and the 1?

Answer 26

that give us 4

Answer 27

12/3

Answer 28

which would simplify to 4.

Answer 29

Good! But we're not simplifying it just yet!

We've gotten 12/3 but now we're subtracting this by 2/3. So \[\ -\frac{2}{3} - \frac{12}{3}\] What does this give us?

Answer 30

-4 2/3?

Answer 31

Ahh, yes you are right. I didn't catch it the first time! Sorry. Instead of writing it in that form, it's easier to leave it in fraction form :)

What would the fraction form by of -4 2/3?

Answer 32

-14/3

Answer 33

Good job, you got it :D

Answer 34

so what would it be ?

Answer 35

so your equation is right, just keep the -14/3 in fraction form since it looks funny otherwise :P

Answer 36

So your equation would then be y = (-2/3)x - 14/3 :)

Answer 37

awesome! thanks!!

Answer 38

Yup!