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# Finding y intercept given slope & point (old)

An old video where Sal finds the y-intercept of the line y=17/13x+b given that the line passes through (5,8). Created by Sal Khan.

Video transcript

The following line passes
through the point 5 comma 8, and the equation of the line
is y is equal to 17/13x plus b. What is the value of
the y-intercept b? So we know that this
point, this x and y value must satisfy this
equation, so we know that when x is equal
to 5, y is equal to 8. So we can say-- so when x is
equal to 5, y is equal to 8. So we can say 8 must be equal
to 17/13 times x times 5 plus b, and then we can solve for b. So if we simplify
this a little bit, we get 8 is equal to--
let's see, 5 times 17 is 50, plus 35 is 85-- is 85/13 plus b. Then to solve for b, we just
subtract 85/13 from both sides. So we have 8 minus 85/13. 85/13 Is equal to b. And now we just have to
subtract these two numbers. So 8 is the same
thing as-- let's see. 80 plus 24 is 104,
so it is 104/13-- this is the same thing
as 8-- minus 85/13, which is going to
be-- let's see. This is 19/13. Is that right? Yes, if this was 105,
then it would be 20/13. So this is 19/13, so it's equal
to 19/13, which is equal to b. So the equation of this
line is going to be y is equal to 17/13x plus 19/13.