Question

Use the intercept method to graph: 3x+4y=-12

Answer 1

So we want to somehow make your equation look like slope-intercept form, which is this:

y = mx + b

Where y is by itself and always positive and the number with x is the slope. Do you think you know how to rearrange your equation to look like that

Answer 2

No

Answer 3

Alright, no problem. So we want to get y by itself. So what do you think would be the first thing to try and do to get y by itself?

Answer 4

Subtract 4?

Answer 5

Well, we would start by moving the 3x to the other side. We cannot subtract 4 because it is multiplying y. If we ever want to remove the 4 with y, we would have to divide. We usually want to divide last, though. So does it make sense if we subtract 3x from both sides?

Answer 6

y=-12-3x/4

Answer 7

Careful. If we divide by 4, everything has to be divided by 4. Like this:
\[\frac{ 4y }{ 4 }=-\frac{ 3x }{ 4 }-\frac{ 12 }{ 4 }\]

Answer 8

That make sense what I did?

Answer 9

Yes. Y=-12/4-3x/4

Answer 10

Right. So -12/4 simplifies to what?

Answer 11

-3/1?

Answer 12

Right. So now we're left with this:
\[y=-\frac{ 3x }{ 4 }-3 \] So now we've done what we wanted to do, we got it to look like
y = mx + b

Now, m is our slope and b is our y-intercept. Do you know what slope and y-intercept are?

Answer 13

Yes. How do you graph this?

Answer 14

Okay, cool. So our y-intercept is -3. So we start like this:



So the slope tells us how much we have to move to get to our next point. So which direction would I move in and how much?