I have a math test tomorow And I don't understand the rate of change. I'm talking about the rate of change assosiated with graphs and cartesian planes. Keep in mind I'm in grade 9 so Nothing uber complicated?
Rate of change = amount of change per second

I don't think I've ever heard the word "cartesian" in my life, and I'm doing my AS levels (Yes, one in maths) right now :/
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Maybe Cartesian is canadian. It's basicly thebig graph with the x and y (Z for 3D) axis in the middle.
The rate of change is the change in one variable (if you're doing grade 9 coordinate plane stuff, say x) with respect to another variable (in this case, y). As y changes a certain amount, x will change an amount relative to that. When you get into calculus that number will be "zero", but for now you don't have to worry about that.

If you have an equation such as y=5x, the change in y is 5 times the change in x. If x increases by 1, y increases by 5, and if x decreases by 2, y decreases by 10.

If you're given a something like a cost equation, say C=\$2x, where x is your number of units, than the rate of change for C relative to x will be \$2, because for every change of 1 in x, the cost changes by \$2.

Note that the rate of change remains the same between y=5x and y=5x+1, or C=\$2x and C=\$2x+\$4. The change in one variable relative to the change in the other remains the same.

If you're dealing with exponents (equations like y=x^2), which I don't think you will be yet, the change is proportional do the other variable. So instead of getting a rate of change like 1/2 or 3, you'll get a rate of change like 3x+1, where the rate of change changes as the other variable changes.

Hope that helps.
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Last edited by jammoe at Jan 24, 2007,
Cartesian is just (x,y) stuff.

I think at your level "rate of change" would just be the gradient of a line at a certain point.

EDIT: Basically what he said^
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Quote by JamieB
Rate of change = amount of change per second

I don't think I've ever heard the word "cartesian" in my life, and I'm doing my AS levels (Yes, one in maths) right now :/

Cartesian is from Renee Descartes who got the whole idea thing for it. It's the coordinate plane with the x/y axes.

Threadstarter: Rate of change is equal to the slope. If the slope is z, then the thing on the y axis changes z units for every one unit of change on the x axis.
y2-y1
_____

x2-x1
Is rate of change not just another term for slope?

m = rise/run

which fits well with

y = mx + b

Trust me, this linear systems stuff is easy. Most people I know find the grade 10 Quadratics unit tough.
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Cartesian is from Renee Descartes who got the whole idea thing for it. It's the coordinate plane with the x/y axes.

Threadstarter: Rate of change is equal to the slope. If the slope is z, then the thing on the y axis changes z units for every one unit of change on the x axis.

So basically "a pair of axes"?

To Muphin, it's y = mx + c

N00b

And yes

When I hear "rate of change" I tend to think physics and time rather than maths.
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Quote by JamieB
So basically "a pair of axes"?

To Muphin, it's y = mx + c

N00b

And yes

When I hear "rate of change" I tend to think physics and time rather than maths.

Right, but Cartesian plane is the proper name for it.

In the States, we learn slope-intercept form as y = mx + b, not that it matters what variables you use seeing as how they just represent numbers.

m = gradient = slope = rise/run = rise/tread = change in y/change in x = deltay/deltax

And you're right, rate of change really is just another word for slope in math, when you apply it to physics it actually matters.
Quote by Muphin
Is rate of change not just another term for slope?

m = rise/run

which fits well with

y = mx + b

Trust me, this linear systems stuff is easy. Most people I know find the grade 10 Quadratics unit tough.

yes but your trying to find the slope which in the case is rate of change