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Find the slope of the linear function defined by the table.

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And they give us a table here.

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They define certain amount, I guess these are shift lengths,

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and then they say how many hours is a half a day, is a

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full day, is two days, is a week, is a month.

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And then they tell us how much money do we make in each of

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those time periods.

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If we work four hours, we make $54, if we work eight hours,

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we make $108, so forth and so on.

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And then they say what does the slope

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represent in this situation?

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So we have to find the slope and figure out what it

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represents.

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So just as a bit of review, slope just equals the change

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in the dependent variable divided by the change in the

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independent variable.

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So how much does a dependent variable change for any amount

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of change of the independent variable?

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In this situation, the dependent variable is the

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amount of money you make because it is dependent on how

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much time you work, this is independent.

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So let's call the independent variable x, the dependent

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variable y.

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So our slope in this situation would be change in y divided

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by change in x.

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So how much does the amount of money I make change when I

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work a certain number of hours, when my hours worked

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change by a certain amount.

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So let's just take some data points here.

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We could take really any of these data points, I'll take

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some of the smaller numbers.

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So let's say if when I go from four to eight hours, so my

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change in x is going to be what?

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If I go from four to eight, might change in x is going to

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be eight minus four, four hours, right?

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So this is going to be my change in x.

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I'm just picking these two points, I could have picked

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four and forty if I wanted, but the math would become more

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complicated.

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But how much does the amount of money earn change if I go

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from four hours to eight hours?

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Well, I go from $54 to $108, so the difference in the

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amount of money I make is $108 minus $54.

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So what is my change in my dependent variable?

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Well, that's going to be $108 minus $54, that's just $54.

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And then what was the change in the

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amount of hours I worked?

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Well, the change in the hours I worked was four hours.

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So, if I work four more hours, I make 54 more dollars.

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Let me put a little equal sign there.

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So what is 54 divided by four?

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So four goes into 54-- looks like there's going to be

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decimal here-- four goes into five one time, one

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times four is four.

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Subtract, you get five minus four is one, bring down this

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four you get 14.

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Four goes into 14 three times, three times four is 12.

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Fourteen minus 12 is two, bring down a 0 right here,

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four goes into 20 five times.

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And of course you have this decimal right here.

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Five times four is 20.

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Subtract, no remainder.

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So this is equal to 13.5, but since we're talking in terms

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of dollars, maybe say $13.50, because that's

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our numerator, right?

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This is money earned, dollars per hour, because that's our

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denominator, dollars per hour.

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So that essentially answers our question.

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What does the slope represent in this situation?

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It represents the hourly wage for working at

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wherever this might be.

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Frankly, for this problem, you didn't even have to take two

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data points.

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We could have said hey, if you work four hours and make $54,

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54 divided by four is 13.50.

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Or we could have said hey, if we work eight hours, we get

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$108, 108 divided by eight is 13.50.

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So you didn't even have to take two data points here, you

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could have just taken any of these numbers divided by any

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of these numbers.

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But hopefully we also learned a little bit

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about what slope is.

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