Slope Example

Algebra

Graphing points, equations and inequalities

Slope

Slope of a line
Slope of a Line 2
Slope and Rate of Change
Graphical Slope of a Line
Slope of a Line 3
Slope Example
Hairier Slope of Line
Identifying slope of a line
Slope and Y-intercept Intuition
Line graph intuition
Average Rate of Change Example 1)
Average Rate of Change Example 2)
Average Rate of Change Example 3)
Average rate of change

Additional content

Algebra: Slope
Algebra: Slope 2
Algebra: Slope 3

Slope Example Slope Example

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Slope Example

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Find the slope of the linear function defined by the table.
And they give us a table here.
They define certain amount, I guess these are shift lengths,
and then they say how many hours is a half a day, is a
full day, is two days, is a week, is a month.
And then they tell us how much money do we make in each of
those time periods.
If we work four hours, we make $54, if we work eight hours,
we make $108, so forth and so on.
And then they say what does the slope
represent in this situation?
So we have to find the slope and figure out what it
represents.
So just as a bit of review, slope just equals the change
in the dependent variable divided by the change in the
independent variable.
So how much does a dependent variable change for any amount
of change of the independent variable?
In this situation, the dependent variable is the
amount of money you make because it is dependent on how
much time you work, this is independent.
So let's call the independent variable x, the dependent
variable y.
So our slope in this situation would be change in y divided
by change in x.
So how much does the amount of money I make change when I
work a certain number of hours, when my hours worked
change by a certain amount.
So let's just take some data points here.
We could take really any of these data points, I'll take
some of the smaller numbers.
So let's say if when I go from four to eight hours, so my
change in x is going to be what?
If I go from four to eight, might change in x is going to
be eight minus four, four hours, right?
So this is going to be my change in x.
I'm just picking these two points, I could have picked
four and forty if I wanted, but the math would become more
complicated.
But how much does the amount of money earn change if I go
from four hours to eight hours?
Well, I go from $54 to $108, so the difference in the
amount of money I make is $108 minus $54.
So what is my change in my dependent variable?
Well, that's going to be $108 minus $54, that's just $54.
And then what was the change in the
amount of hours I worked?
Well, the change in the hours I worked was four hours.
So, if I work four more hours, I make 54 more dollars.
Let me put a little equal sign there.
So what is 54 divided by four?
So four goes into 54-- looks like there's going to be
decimal here-- four goes into five one time, one
times four is four.
Subtract, you get five minus four is one, bring down this
four you get 14.
Four goes into 14 three times, three times four is 12.
Fourteen minus 12 is two, bring down a 0 right here,
four goes into 20 five times.
And of course you have this decimal right here.
Five times four is 20.
Subtract, no remainder.
So this is equal to 13.5, but since we're talking in terms
of dollars, maybe say $13.50, because that's
our numerator, right?
This is money earned, dollars per hour, because that's our
denominator, dollars per hour.
So that essentially answers our question.
What does the slope represent in this situation?
It represents the hourly wage for working at
wherever this might be.
Frankly, for this problem, you didn't even have to take two
data points.
We could have said hey, if you work four hours and make $54,
54 divided by four is 13.50.
Or we could have said hey, if we work eight hours, we get
$108, 108 divided by eight is 13.50.
So you didn't even have to take two data points here, you
could have just taken any of these numbers divided by any
of these numbers.
But hopefully we also learned a little bit
about what slope is.

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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

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At 2:33, Sal says "double bonds" but should say "single bonds."

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