The rate of change in algebra is the ratio ( fraction ) that shows how the two variables in an equation are related. For example, if you are comparing the# of identical items (x) in a cup to the weight of the cup ( y ) , the rate of change would be the weight of one of the items. If the items each weigh 2 oz then each time an item is added the weight would increase by 2 oz. Thus the rate of change is 2/1. The equation might look like
y = 2x + 3
where the coefficient of x ( 2 ) is the rate of change and the constant , 3, is the weight of the empty cup.
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Slope in algebra refers to the rate of change of a function at a given point. This can be used in physics, where on a graph that shows the change in velocity, the value of the slope is equal to the acceleration at that moment in time.
If you are talking about linear graphs, m refers to the gradient (aka slope or rate of change).
The same way you do for simple algebra. The complication on each side don't change the rules; you are still doing algebra.
You use it to find how long it takes to double or triple the amount you put in with rate and time. It's in Algebra 2.
The formula for rate is distance equals rate times time. The rate is a ratio that compares two different kinds of numbers, for example: miles per hour.