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## Lesson 11: Equations of all kinds of lines

Current time:0:00Total duration:5:07

## Video transcript

We're asked to convert these
linear equations into slope-intercept form and then
graph them on a single coordinate plane. We have our coordinate
plane over here. And just as a bit of a review,
slope-intercept form is a form y is equal to mx plus b,
where m is the slope and b is the intercept. That's why it's called
slope-intercept form. So we just have to algebraically
manipulate these equations into this form. So let's start with line A,
so start with a line A. So line A, it's in standard form
right now, it's 4x plus 2y is equal to negative 8. The first thing I'd like to do
is get rid of this 4x from the left-hand side, and the best way
to do that is to subtract 4x from both sides
of this equation. So let me subtract 4x
from both sides. The left hand side of the
equation, these two 4x's cancel out, and I'm just left
with 2y is equal to. And on the right-hand side I
have negative 4x minus is 8, or negative 8 minus 4, however
you want to do it. Now we're almost at
slope-intercept form. We just have to get rid of this
2, and the best way to do that that I can think of is
divide both sides of this equation by 2. So let's divide both
sides by 2. So we divide the left-hand side
by 2 and then divide the right-hand side by 2. You have to divide
every term by 2. And then we are left with y is
equal to negative 4 divided by 2 is negative 2x. Negative 8 divided by
2 is negative 4, negative 2x minus 4. So this is line A, let me
graph it right now. So line A, its y-intercept
is negative 4. So the point 0, negative
4 on this graph. If x is equal to 0, y is going
to be equal to negative 4, you can just substitute
that in the graph. So 0, 1, 2, 3, 4. That's the point
0, negative 4. That's the y-intercept
for line A. And then the slope
is negative 2x. So that means that if I change
x by positive 1 that y goes down by negative 2. So let's do that. So if I go over one in the
positive direction, I have to go down 2, that's what a
negative slope's going to do, negative 2 slope. If I go over 2, I'm going
to have to go down 4. If I go back negative 1, so
if I go in the x direction negative 1, that means in the y
direction I go positive two, because two divided by negative
one is still negative two, so I go over here. If I go back 2, I'm
going to go up 4. Let me just do that. Back 2 and then up 4. So this line is going
to look like this. Do my best to draw it,
that's a decent job. That is line A right there. All right, let's do line B. So line B, they say 4x is equal
to negative 8, and you might be saying hey, how do I
get that into slope-intercept form, I don't see a y. And the answer is you won't be
able to because you this can't be put into slope-intercept
form, but we can simplify it. So let's divide both sides
of this equation by 4. So you divide both sides
of this equation by 4. And you get x is equal
to negative 2. So this just means, I don't care
what your y is, x is just always going to be equal
to negative 2. So x is equal to negative 2 is
right there, negative 1, negative 2, and x is just always
going to be equal to negative 2 in both directions. And this is the x-axis,
that's the y-axis, I forgot to label them. Now let's do this last
character, 2y is equal to negative eight. So line C, we have 2y is
equal to negative 8. We can divide both sides of this
equation by 2, and we get y is equal to negative 4. So you might say hey, Sal, that
doesn't look like this form, slope-intercept
form, but it is. It's just that the slope is 0. We can rewrite this as y is
equal to 0x minus 4, where the y-intercept is negative
4 and the slope is 0. So if you move an arbitrary
amount in the x direction, the y is not going to change,
it's just going to stay at negative 4. Let me do a little bit neater. y is just going to stay
at negative 4. Or you can just interpret it as
y is equal to negative 4 no matter what x is. So then we are done.