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We are asked which of these lines are parallel.

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So parallel lines are lines that have the same slope, and

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they're different lines, so they never, ever intersect.

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So we need to look for different lines that have the

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exact same slope.

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And lucky for us, all of these lines are in y equals mx plus

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b or slope-intercept form, so you can really just look at

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these lines and figure out their slope.

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The slope for line A, m is equal to 2.

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We see it right over there.

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For line B, our slope is equal to 3, so these two guys are

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not parallel.

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I'll graph it in a second and you'll see that.

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And then finally, for line C-- I'll do it in purple-- the

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slope is 2.

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So m is equal to 2.

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I don't know if that purple is too dark for you.

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So line C and line A have the same slope, but they're

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different lines, they have different y-intercepts, so

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they're going to be parallel.

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And to see that, let's actually graph all of these

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characters.

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So line A, our y-intercept is negative 6.

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So the point 0, 1, 2, 3, 4, 5, 6.

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And our slope is 2.

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So if we move 1 in the positive x direction, we go up

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2 in the positive y direction.

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One in x, up 2 in y, if we go to in x, we're going

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to go up 4 in y.

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And I can just do up 2, then we're going to go 2, 4, and

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you're going to see it's all on the same line, so line A is

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going to look something like-- do my best to draw it as

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straight as possible.

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Line A-- I can do a better version than that-- line A is

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going to look like-- well, that's about just as good as

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what I just drew-- that is line A.

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Now let's do line B.

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Line B, the y-intercept is negative 6.

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0, negative 6.

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So it has the same y-intercept, but its slope is

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3, so if x goes up by 1, y will go up by 3.

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

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If x goes up by 2, y is going to go up by 6.

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2, 4, 6.

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So this line is going to look something like this.

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Trying my best to connect the dots.

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It has a steeper slope, and you see that when x increases,

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this blue line increases by more in the y direction.

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So that is line B-- and notice, they do intersect,

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there's definitely not two parallel lines.

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And then finally, let's look at line C.

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The y-intercept is 5.

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So 0, 1, 2, 3, 4, 5.

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The point 0, 5, its y-intercept.

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And its slope is 2.

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So you increase by 1 in the x direction, you're going to go

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up by 2 in the y direction.

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If you decrease by 1, you're going to go

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down 2 in the y direction.

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If you increase by, well, you're going to go to that

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point, you're going to have a bunch of these points.

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And then if I were to graph the line-- let me do it one

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more time-- if I were to decrease by two, I'm going to

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have to go down by 4, right?

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Negative 4 over negative 2 still a slope of

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2, so 1, 2, 3, 4.

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And I can do that one more time, get right over there.

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And then you'll see the line.

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The line will look like that, it will look just like that.

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And notice that line C and line A never intersect.

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They have the exact same slope.

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Different y-intercepts, same slope, so they're increasing

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at the exact same rate, but they're never going to

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intersect each other.

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So line A and line C are parallel.

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