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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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- 0:48Is 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?(6 votes)
- 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
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.(6 votes)
- So what is the slope of a slide(4 votes)
- Is time always the independent variable? is it ever the dependent variable?(4 votes)
- 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."(4 votes)
- was this using the formula m=y2-y2/x2-x1?(3 votes)
- (accidentally posted in comments)
You mean m = y2 - y*1* / x2 - x1?
I believe so :)
If you were to rearrange it, Sal technically took
y2 ($108.00) - y1($54.00) / x2 (8) - x1 (4)
That's a really good way to think about it!(2 votes)
- 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?(2 votes)
- slope = rise above run
s = rise/run
now just flip the equation around by *run on both sides - that gives you
s * run = rise(4 votes)
- Wait so the dollar sign does not have one line in the middle like $?
Or is it used to mean something else?(2 votes)
- what is the reason that in this particular example you can compute slop using just one data point ?(2 votes)
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.