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### Course: Algebra (all content)>Unit 3

Lesson 11: Interpreting linear functions and equations

# 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?

• 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
• So what is the slope of a slide
• slope = rise/run. Rise being the "y" axis and run being the "x" axis.
• 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."
• I don’t really understand this that much.
• 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?
• slope = rise above run
s = rise/run
now just flip the equation around by *run on both sides - that gives you
s * run = rise
• Can change also be called delta?
• what is the reason that in this particular example you can compute slop using just one data point ?
• Well, there's really a second data point at (0,0). If you work zero hours, you earn zero pay.