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Write the equation of a line that has a slope of one-third,

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and contains the point negative 12, negative 14-thirds.

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So the equation of a line we can write as 'y' is equal to...

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...'mx' plus 'b'. This is in slope-intercept form,

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where 'm' is our slope, and 'b' right over here is our y-intercept.

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And they have actually given us our slope.

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Our slope, they tell us, is one-third. So we know that 'm' is going to be one-third,

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so we know that 'y' is equal to one-third 'x' plus 'b'.

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And so now we just have to solve for 'b',

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and the way we can solve for 'b' is that we know this line contains the point negative 12, negative 14/3.

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So when 'x' is equal to negative 12, 'y' is equal to negative 14/3.

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So lets write that down: negative 14/3 is going to be equal to one-third our slope times our 'x' value,

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which is negative 12 times negative 12, and then plus 'b'.

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So when 'x' is negative 12, we know that 'y' is equal to negative 14/3,

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and we also know that the slope is one-third. That's the 'm' in 'mx'+'b'.

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So now we can solve for 'b'.

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The left hand side negative 14/3 is equal to one-third times negative 12.

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One-third times negative 12 is negative 4, so this is negative 4 plus 'b'.

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Let me write that plus 'b' in the same colour that I started with.

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And now just isolate 'b' on the right hand side, we can add 4 to both sides.

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I want to get rid of this negative 4 so lets add 4 to both sides.

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So plus 4, plus 4, we are left with, on the right hand side, we are left with just a 'b'.

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'b' is equal to...

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On the left hand side we have 4.

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4 I can re-write because I'm going to have to add 4 to negative 14/3.

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So I want a common denominator. 4 is the same thing as 12/3,

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So 4 is 12/3, minus 14/3...

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...so I just want to be clear: I just re-wrote the 4 as 12/3.

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So 12/3 minus 14/3, or negative 14/3 plus 12/3, is going to give us...

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...we have the same denominator of 3, so we are going to have 12 minus 14 is negative 2.

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So we have -2/3 is equal to 'b'.

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So the equation of the line we figured out.

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They gave us the slope and now we just figured out the y-intercept using the information right over here.

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So the equation of our line is going to be 'y' is equal to one-third 'x'...

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...we got the one-third from the problem.

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One-third 'x' plus 'b', 'b' is negative two-thirds...

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...so I can just write negative 2 over 3.

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And we are done.