Slope: Rate of Change of Two Variables
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00:01: Okay, we're gonna talk about the rate of change of two variables. So when we talk about the rate of change of two variables, what are we actually talking about? Well, rate of change usually implies slope, so we're talking about the slope. Well, how do you find slope again? If you remember, the slope is the change in Y, or your dependent variable, over the change in X, or your independent variable. And usually you'll see this written as delta Y over delta X. 00:37: Okay, so we wanna find the slope, given that for every unit X increases, Y decreases five units. So we have our two variables, we have X and we can see that it increases every one unit and we can see Y decreases every five units when X increases one. So how do we find the slope of this? It's gonna be the change in Y over the change in X. So what is Y doing? It is decreasing five units. And what is X doing? It is increasing one unit. So we can write this as negative five over one, or negative five. 01:17: Here we know that a car travels 140 miles every two hours, what is the speed of the car? So the speed is another rate of change. And to find the speed, it's the change in distance over a time interval. So what do we know? It goes 140 miles every two hours, so the change in distance is 140 miles and the time is two hours. So this is gonna be 70 miles per hour.
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Question 1
Slope is found by dividing the change in ____ by the change in ____.
Responses
A x; yx; y
B y; xy; x
Question 2
What is the slope in the example?
Responses
A 5/15/1
B -5/1-5/1
Question 3
The speed of the car is ______ miles per hour.
Responses
A 7070
B 6565
C 6060
Question 1: Slope is found by dividing the change in y by the change in x.
Question 2: The slope in the example is -5/1 or -5.
Question 3: The speed of the car is 70 miles per hour.