Question

What is the equation of the line that passes through the point (1, 6) and has a slope of 3?

Answer 1

y = 3x + 5
y = 3x + 3
y = 3x - 17
y = 3x - 5

Answer 2

Use the equation y=mx+b and plug in the slope, m, and the points x and y to solve for b.

Answer 3

how do i set up mx+b when i don't have a second number?

Answer 4

so you know Y=6 X=1 and M=3 so then you plug those in. 6=3(1)+b now you are able to solve for b. do that and then tell me what you get for b

Answer 5

then we will go onto the final step

Answer 6

were you able to find b?

Answer 7

not really :(

Answer 8

It's find we will work through it together.

Answer 9

So, you have the equation:

6=3(1)+b and now you need to simplify both sides of the equation which would give you
6=3+b now you need to isolate b and you do that by subtracting 3 from both sides which would give you
3=b now you have solved for b

The final step is to plug b and m back into the equation giving you the final answer of

y=3x+3

Answer 10

Thanks! I understand more now. Can you please help me with another?

Answer 11

Sure! what is your question?

Answer 12

its kind of similar:

What is the equation of the line that passes through the points (-3, 2) and (-5, 8)?

Answer 13

what we would do now is line them up in mx+b format

Answer 14

For this problem, I would use the Point-Slope form. Are you familiar with this form?

Answer 15

Somewhat

Answer 16

Okay. so we will start with the equation. (first y- second y)=m(first x- second x) because we now lets plug in the variables we already have.

Answer 17

(2-8)=m(-3--5) which will give us
-6=m(2) or -6=2m from there we want to isolate m so we divide both sides by 2 giving us
-3=m now we have solved for m

Answer 18

Do you need the equation in y=mx+b form or point slope form?

Answer 19

Is there a right or wrong answer to that? :s

Answer 20

Nope! I was just wondering if your class required it to be in a certain form. I can show you both ways!

Answer 21

There's no specific way for it to be done. I would prefer mx+b because I'm most familiar with that, but then again it would be best to learn other ways too

Answer 22

So, now that you have all of the variables, you can plug them into the equation.
(you can chose which coordinate pair to plug in because they will both give you the same answer)

So point slope form would look like this:
(y-2)=-3(x--3) or (y-2)=-3(x+3) now once you have it in this form you are able to change it into y= mx+b form

Answer 23

Here's how

Answer 24

First you need to simplify both sides of the equation so you will end up with
y-2=-3x-9 next you need to isolate y so you add to both sides which would give you
y=-3x-7 and that is your final answer now that it is in y=mx+b form!

Answer 25

i get what you're saying, but that's not a choice for the question

Answer 26

oh. maybe i made a math mistake. what are your options?

Answer 27

3x - y = -11
3x + y = - 7
3x + y = 5
x + 3y = 3

Answer 28

B is similar

Answer 29

the answer i got was correct and you are right it is b. The reason they look different is because the options are in standard form (ax+by=c) so if you solved for c, which in this case is -7 you would get the answer 3x+y=-7

Answer 30

That's what I figured :) thanks so much for helping me! before you go, would I solve this in the same way?

Select the equations that are parallel and perpendicular to y = -3x - 1 and that pass through the point (3, 1).

Answer 31

Yes! it would be similar to the first problem we solved. But first you have to find what the slopes would be for each line. Do you know how to do that?

Answer 32

maybe

-3 - 3
--------
1 - 1

Answer 33

so yes that is an option for finding the slope. but because you know the lines are going to be parallel and perpendicular there is an even easier way to figure them out. If lines are parallel, then they have the same slope. So, for the parallel line the slope will be -3. When lines are perpendicular, the slope will be the opposite and the reciprocal. So for the perpendicular line, the slope would be

Answer 34

now that you have the slopes, you can find both of the lines just like in the first problem!

Answer 35

parallel: y = -3x + 6
perpendicular: y = 1/3 x + 2 2/3 ?

Answer 36

is this correct?

Answer 37

would you mind typing out the equations you used because i'm getting different answers

Answer 38

i'm not really sure, i tried to solve this mentally

Answer 39

did you get options for this problem?

Answer 40

yes