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# Slope-intercept equation from slope & point: fractions (old)

An old video where Sal finds the slope-intercept form of a line that has a slope of ⅓ and goes through the point (-12,-14/3). Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Write the equation of the
line that has a slope of 1/3 and contains the point
negative 12, negative 14/3. So the equation of
a line we can write as y is equal to mx plus b. This is in slope-intercept
form, where m is our slope and b right over here
is our y-intercept. And they have actually
given us our slope. Our slope, they tell us, is 1/3. So we know that m
is going to be 1/3. So we know that y is
equal to 1/3 x plus b. And so now we just
have to solve for b. And the way we can solve for
b is that we know this line contains the point
negative 12, negative 14/3. So when x is equal
to negative 12, y is equal to negative 14/3. So let's write that down. Negative 14/3 is going
to be equal to 1/3-- our slope-- times
our x value, which is negative 12-- times
negative 12-- and then plus b. So when x is
negative 12, we know that y is equal
to negative 14/3. And we also know that
the slope is 1/3. That's the m in mx plus b. So now we can just solve for b. The left-hand side-- I'll just
leave it as negative 14/3-- is equal to 1/3
times negative 12. 1/3 times negative
12 is negative 4, so this is negative 4, plus b. Let me write the plus
b in that same color that I had started it with. Plus b. It looks like a yellow color. And now, to isolate b
on the right-hand side, we can add 4 to both sides. I want to get rid
of this negative 4. So let's add 4 to both sides. So plus 4, plus 4-- on
the right-hand side, we're left with just a b. b is equal to-- on the
left-hand side, we have 4. 4 I can rewrite. Because I'm going to have
to add 4 to negative 14/3. So I want a common denominator. 4 is the same thing as 12/3. So 4 is 12/3, minus 14/3. So I just want to be clear. I just rewrote the 4 as 12/3. So 12/3 minus 14/3, or
negative 14/3 plus 12/3, is going to give us-- well, we
have the same denominator of 3. So we're going to have 3. 12 minus 14 is negative 2. So we have negative
2/3 is equal to b. So the equation of the
line we figured out. They gave us the slope. And now we just figured
out the y-intercept using this information
right over here. So the equation of
our line is going to be y is equal to 1/3 x-- we
got the 1/3 from the problem-- plus b. b is negative 2/3. So I could just write minus 2/3. And we are done.