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Linear equations word problems: earnings

Sal finds the slope of a linear relationship between the number of work hours and the money earned. He then interprets what this slope means in that context. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • aqualine ultimate style avatar for user DIMEJI BASSIR
    So what is the slope of a slide
    (6 votes)
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  • spunky sam blue style avatar for user Samir Gunic
    Is this what "direct relationship" means? What do you call that other thing, something like "inverse relationship" or similarly?

    ... or is it that "direct relationship" is when you have an upwards sloping line? And then "reverse relationship" or whatever you call it, is when you have a downwards sloping line?
    (5 votes)
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    • starky ultimate style avatar for user Anuj
      yeah you got it but a small correction .Both the downward and upward sloping (linear eqn)line are direct variation. because when x increases y also increases
      consider y+3x=0.when x=1,y=-3
      x=2,y=-6
      consider you're doing a mistake,and teacher reduces 3 point for each one
      the for 1mistake you get -3
      2mistake you get-6
      but in indirect variation
      1mistake you get -3
      2 mistake you get -1.5
      3 mistake you get-1
      here you can say when mistake increases my reducing point decreases
      as mistake increase negative point inc.
      (5 votes)
  • duskpin ultimate style avatar for user Dad
    thats pretty cool now i understand
    (6 votes)
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  • leaf green style avatar for user Kate
    Is time always the independent variable? is it ever the dependent variable?
    (3 votes)
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    • female robot grace style avatar for user C C
      No, it depends on the set up. Most that you will see do have time as the independent variable because translated to word problems they read "For every unit of time that passes something happens." It can go the other way. I just got a time as dependent variable example in the function playlist. It was: "Jack is rowing a kayak. If the current is 3km/h against him it will take 2 hours to cross the lake..." So that's an example of word problems of the form "Under some condition measured as x, it will take y units of time to achieve; when the condition changes, the time (dependent) changes too."
      (3 votes)
  • marcimus red style avatar for user Marcimus when the imposter is susඞඞ
    how do u know which one is the dependent variable and which one is the independent variable
    (3 votes)
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    • mr pants purple style avatar for user The Purple Bear
      the independent variable is the variable that you "input". For example, if you work 5 hours a day, you can get 50 dollars by the end of the day. If you work more than 5 hours a day, say 10, you can get 100 dollars by the end of the day. The amount of hours you work is something that you control and the amount of money you get is dependent on the time you work. The amount of hours you work is the independent variable, the amount of money you get is the dependent variable.
      (3 votes)
  • mr pink red style avatar for user NRODemarco
    So I know the slope and the run. How do I find the rise? Slope is 48% and run is 124m how do I solve?
    (1 vote)
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  • female robot ada style avatar for user Arlene
    Wait so the dollar sign does not have one line in the middle like $?
    Or is it used to mean something else?
    (1 vote)
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  • blobby green style avatar for user Nir
    what is the reason that in this particular example you can compute slop using just one data point ?
    (1 vote)
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  • ohnoes default style avatar for user jameswebb
    how do you tell what the slope is?
    (1 vote)
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  • starky ultimate style avatar for user Gabriel Barberini
    Why the point-slope form seems not to work for descendant graphs ?

    At least at 'Linear equations word problems: graphs' exercises.

    Try this:

    First point: 50,200
    Second point: 25,400
    m = 8 (200/25)

    You want to find the Y when X = 0, then you use the point-slope formula:
    (y-b) = m(x-a)
    (y-200) = 8(0-50)

    At the end you'll have y = -200

    Which is not the number of y when x is 0, because in this example y is equal to 600 when x is 0.

    Edit: Found out that my slope is wrong, it should be -8 not 8. Thanks @Kim Seidel for the feedback!
    (1 vote)
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Video transcript

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.