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.

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