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Current time:0:00Total duration:3:24

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

Video transcript

right the equation of the line that has a slope of 1/3 and contains the point negative 12 negative 14 thirds so the equation of the 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 over 3 so when X is equal to negative 12 when X is equal to negative twelve Y is equal to negative 14 over 3y is equal to negative 14 over 3 so let's write that down negative 14 over 3 is going to be equal to one third 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 plus B so when X is negative 12 we know that Y is equal to negative 14 thirds and we also know that the slope is 1/3 that's the M and MX plus B so now we can just solve for B the left-hand side so I'll just leave it as negative 14 over 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 started it with plus B plus looks like a yellow color plus B and now just 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 we are left with on the right hand side we're left with just a B B is equal to on the left hand side we have four four I can rewrite it cuz I'm going up two I'm going to have to add 4 to negative 14 over 3 so I want a common denominator 4 is the same thing as 12 over 3 so 4 is 12 over 3 minus 14 over 3 minus 14 over 3 so I just want to be clear I just rewrote the 4 as 12 over 3 so 12 over 3 minus 14 over 3 or negative 14 over 30 plus 12 over 3 is going to give us well we have the same denominator of 3 so we're going to have 3 12 minus 4 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 a 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 1/3 X plus B B is negative 2/3 so I can just write minus 2 over 3 and we are done