# Parallel lines from equation | Mathematics I | High School Math | Khan Academy

We are asked which of these

lines are parallel. So parallel lines are lines that

have the same slope, and they’re different lines, so they

never, ever intersect. So we need to look for different

lines that have the exact same slope. And lucky for us, all of these

lines are in y equals mx plus b or slope-intercept form, so

you can really just look at these lines and figure

out their slope. The slope for line A,

m is equal to 2. We see it right over there. For line B, our slope is equal

to 3, so these two guys are not parallel. I’ll graph it in a second

and you’ll see that. And then finally, for line C–

I’ll do it in purple– the slope is 2. So m is equal to 2. I don’t know if that purple

is too dark for you. So line C and line A have the

same slope, but they’re different lines, they have

different y-intercepts, so they’re going to be parallel. And to see that, let’s actually

graph all of these characters. So line A, our y-intercept

is negative 6. So the point 0, 1,

2, 3, 4, 5, 6. And our slope is 2. So if we move 1 in the positive

x direction, we go up 2 in the positive y direction. One in x, up 2 in y, if we

go to in x, we’re going to go up 4 in y. And I can just do up 2, then

we’re going to go 2, 4, and you’re going to see it’s all on

the same line, so line A is going to look something like–

do my best to draw it as straight as possible. Line A– I can do a better

version than that– line A is going to look like– well,

that’s about just as good as what I just drew–

that is line A. Now let’s do line B. Line B, the y-intercept

is negative 6. 0, negative 6. So it has the same y-intercept,

but its slope is 3, so if x goes up by 1,

y will go up by 3. So x goes up by 1,

y goes up by 3. If x goes up by 2, y is

going to go up by 6. 2, 4, 6. So this line is going to look

something like this. Trying my best to connect

the dots. It has a steeper slope, and you

see that when x increases, this blue line increases by

more in the y direction. So that is line B– and notice,

they do intersect, there’s definitely not

two parallel lines. And then finally, let’s

look at line C. The y-intercept is 5. So 0, 1, 2, 3, 4, 5. The point 0, 5, its

y-intercept. And its slope is 2. So you increase by 1 in the x

direction, you’re going to go up by 2 in the y direction. If you decrease by 1,

you’re going to go down 2 in the y direction. If you increase by, well, you’re

going to go to that point, you’re going to have

a bunch of these points. And then if I were to graph the

line– let me do it one more time– if I were to

decrease by two, I’m going to have to go down by 4, right? Negative 4 over negative

2 still a slope of 2, so 1, 2, 3, 4. And I can do that one more time,

get right over there. And then you’ll see the line. The line will look like that,

it will look just like that. And notice that line C and

line A never intersect. They have the exact

same slope. Different y-intercepts, same

slope, so they’re increasing at the exact same rate, but

they’re never going to intersect each other. So line A and line

C are parallel.

thanks

Subscribed, This really helps me

Can you make 3-4-5 grade videos too?

Bull shit

pls help me I don't understand what ur explaining.pls do u have a friend of urs in Cameroon

Then how does the +/- b matter then?