Question

Write an equation of the line containing the given point and parallel to the given line.
(-2,8); 7x=5y+6

Answer 1

If two lines are parallel, what is the relation between their slopes?

Answer 2

are they equal distance?. i dunno im horrible with math, not one of my strong points

Answer 3

It's okay :) Two parallel lines have equal slopes. So,

y = 3x + 135
y = 3x + 2

Those two are parallel lines, because they the same slope (3).

Let's focus on the problem below, since you'll have to use the same technique to get the equation they give you in y = mx + b form here.

Answer 4

So now you have 7x = 5y + 6.

Since we need the slope, we need to solve for y again.

Answer 5

okay so would we need to subtract 6 from both sides?

Answer 6

Yep, that's the first step.

Answer 7

-6+7x=5y

Answer 8

or 5y=7x-6

Answer 9

Right. What's next?

Answer 10

get the y by itself

Answer 11

Exactly. So since the y is multiplied by 5, how do we get it by itself?

Answer 12

divide

Answer 13

Right. So we divide each part of the right by 5; what do we get?

Answer 14

y=7/5x-6/5

Answer 15

Boom! Exactly.

So now we know what the slope of a parallel line would have to be. What is it?

Answer 16

7/5

Answer 17

Right. So now we'll need another equation that looks like:

y = 7/5x + b

Does that make sense?

Answer 18

yea that does

Answer 19

Ok, and now they've given us a point that the line goes through, so we can plug in the x and y and solve for b.

Answer 20

okay so 8=7/5(-2)+b

Answer 21

is that right

Answer 22

Absolutely!

Answer 23

So now what do I do?

Answer 24

So we need to figure out what b is, right? How should we do that?

Answer 25

um get b by itself?

Answer 26

Exactly. So what's the first step?

Answer 27

multiply 7/5(-2)

Answer 28

Ok, what does that equal?

Answer 29

-6/5

Answer 30

Not quite. Remember you are multiplying 7/5 by -2. Do you know how to multiply fractions?

Answer 31

not really is it common denominators at all?

Answer 32

That is actually for adding and subtracting. Multiplication is much easier. You are multiplying 7/5 by -2. Remember that -2 is the same as -2/1, which means you have \[\frac{7}{5} \times \frac{-2}{1}\] then you just multiply straight across. What do you get?