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Well, I had to stop that last presentation because

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I ran out of time.

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But now we can start up right where we left off.

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So far, we had figured out the slope and it made sense to

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us because we figured out the slope was minus 4/3.

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You could look at it two ways.

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When the run is 3, the rise is negative 4.

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So rise we went down by negative 4, we ran 3, and

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you can keep doing that on the line and you'll keep

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ending up on the line.

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You could've also gone down 8 and then moved over 6.

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Or you could move over 6 and go down 8.

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If you went down 8 you would've showed up here.

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Then you would've come down back here.

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Whatever the slope is, if you change the y by the rise, and

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you change the run by the x, you should end up

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on the line again.

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I know I'm doing this over and over again, but I think

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it'll slowly sink in.

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But anyway, where we left off we were going to solve for b so

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that we could figure out the final equation for this line.

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Well, just like we did the last time, we just have to

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substitute a y or an x that we know works for this line.

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We know either of these coordinates will work,

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and then we solve for b.

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Let's try this first one: 2 comma negative 3.

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So y is negative 3.

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Don't get confused between x and y.

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y is negative 3 equals minus 4/3 times x, which is 2.

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Plus b.

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And then we get negative 3 equals negative 8/3 plus b.

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And then we get b is equal to-- well, 3 is equal to minus 9/3.

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And then I'm just going to put this on the other side.

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So that's plus 8/3.

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So we get minus 1/3 is the y-intercept.

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So the equation of this line is y is equal to minus 4/3 x and

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then this y-intercept is minus 1/3.

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I know this is extremely messy, but the equation of this line

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once again, is y equals minus 4/3 x minus 1/3.

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Now let's look at the graph and see if that makes sense.

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Well, let's see.

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The y-intercept is right here.

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That's where you intersect the y-axis at the point.

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And we would know exactly what that point is.

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It's 0 comma negative 1/3.

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That's the y-intercept, and it makes sense.

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And even when you look at an equation it's pretty obvious

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that this is going to be the y-intercept because when x

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equals 0 this term gets crossed out.

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Because 0 times negative 4/3.

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And then y would equal negative 1/3.

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Let's do one more just to bore you.

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And because my wife is a resident and she works 30

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hours of time and I have nothing better to do.

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All right.

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Let me put that graph back there.

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I joke, but you don't realize that it's true.

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Let's put the graph back there and I'm going to do

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another random points.

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I'm going to go a little faster this time.

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So let's say I had negative 8 comma 5 and I had-- let me

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think of a good one-- 2 comma-- I'm just going

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to make up a number.

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2 comma, let's say 0.

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That's interesting.

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2 comma 0.

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So let's graph negative 8 comma 5.

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1, 2, 3, 4, 5, 6, 7, 8.

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1, 2, 3, 4, 5.

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Right there is minus 8 comma 5.

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And then 1, 2, and then 0 is right here.

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So that's 2 comma 0.

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And now let me draw the line.

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Oh my God.

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I thought I was using the line tool.

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That's horrendous.

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I wish there was an undo tool.

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That was horrendous.

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That was unacceptable.

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That's a little bit better.

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Just so you know that the line doesn't end there.

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Lines go on forever and ever in the coordinate axis.

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There you go.

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OK.

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So let's figure out the slope of this line.

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Well, change in y over change in x.

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I'm using the line tool again.

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I'm a spaz today.

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Let's take this as a starting point.

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We'll get 5 minus 0.

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y sub 1 minus y sub 2.

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Over x sub 1-- minus 8 minus 2.

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So it equals 5 over minus 10.

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And that equals minus 1/2.

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So that means for every 2 we go over, we go down 1.

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Well, for every 1 we go down, we go over 2,

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which makes sense.

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If we go down 2, we'll go over 4.

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Because 2/4 is the same thing as 1/2.

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I hope that makes sense to you.

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I know this is a downwards sloping line.

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So that was fast.

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So we know that the equation of the line so far is y is

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equal to minus 1/2 x plus b.

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Now we just solve for b.

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Let's substitute some numbers in here.

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Well, let's use this one.

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This is interesting: 2 comma 0.

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So y is 0.

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Equals minus 1/2 times 2 plus b.

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Well, 0 is equal to and this is minus 1 plus b.

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And we get b equals 1.

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This is a pretty easy problem.

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So now we get y is equal to minus 1/2 x plus 1.

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OK, now let's see if this actually looks right

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on our problem.

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Well, this is telling us that the y-intercept

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is at the point 0, 1.

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0, 1 is right here.

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And our algebra confirms our drawing.

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This is the y-intercept and we see that the

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slope is negative 1/2.

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It makes sense because it's a downward sloping line,

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but it's not too steep.

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For every 1 that we go down, we go over 2.

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So that's negative 1/2.

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Or you could say for every 2 we run, we rise negative 1.

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Either one, we end up on a line again.

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So I hope that helps.

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I think you are definitely ready to do a lot of these

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slope problems that we have on the Khan Academy.

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So I hope you have fun and if you any questions you can

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attend one of the seminars.

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Have fun.