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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.

## Want to join the conversation?

• So what is the slope of a slide
• slope = rise/run. Rise being the "y" axis and run being the "x" axis.
• 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?
• 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.
• thats pretty cool now i understand
• Is time always the independent variable? is it ever the dependent variable?
• 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."
• how do u know which one is the dependent variable and which one is the independent variable
• 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.
• Can change also be called delta?
• 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)
• slope = rise above run
s = rise/run
now just flip the equation around by *run on both sides - that gives you
s * run = rise
• Wait so the dollar sign does not have one line in the middle like \$?
Or is it used to mean something else?
(1 vote)
• I think it can be denoted and written with both a single line in the middle or double lines in the middle.