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What is the relationship among proportional relationship lines rate of change and slope?
The rate of change is the same as the slope.
How does the slope differ from average rate of change?
They are the same for a straight line but for any curve, the slope will change from point to point whereas the average rate of change (between two points) will remain the same.
Does rate of change mean the same as slope?
For continuous functions, yes.
Can a rate change and the slope of the line be different quantities?
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
What is the rate of change between any two points on a line?
it is the same as the slope, which can be found either graphically (rise over run) or algebraically using the formula (y2-y1)/(x2-x1)
What is the relationship between unit rates slopes and constant rate of change?
Unit rate, slope, and rate of change are different names for the same thing. Unit rates and slopes (if they are constant) are the same thing as a constant rate of change.
Is rate of change the same as slope?
Yes, Rate of change is slope
What is the relationship among proportional relationship lines rate of change and slope?
The rate of change is the same as the slope.
How does the slope differ from average rate of change?
They are the same for a straight line but for any curve, the slope will change from point to point whereas the average rate of change (between two points) will remain the same.
Does rate of change mean the same as slope?
For continuous functions, yes.
How is slope and constant rate of change the same?
Slope is known as rise over run. Rise means the amount of units the y-value (or second dimension) has traveled up the y-axis or down the y-axis. Run means the amount of units the x-value (the first dimension) has traveled forwards or backwards on the x-axis. Take a slope of 2 (can also be written as 2/1) that means it goes up two units as it goes over 1 unit for the whole entire graph. A slope of 5/7 means it goes with a y-value of 5 up and an x-value of 7 over. This can be done for any number even negative numbers. Ok... so now to relate it to a constant rate of change. Imagine the dimensions (x and y values) go on for an infinite amount. The slope will be constant throughout infinity. It will always have the same rise over run... It will always be constant. The rate of change is equivalent to the saying "rise over run". Since the slope is constant over infinity the constant rate of change is the same thing across infinity.
Can a rate change and the slope of the line be different quantities?
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
How does finding slope compare to finding the rate of change between two variables in a linear relationship?
The slope of a line is the same thing as the rate of change between two variables in a linear relationship.
What if the rate of change is a measure of how fast the function is increasing or decreasing what does the slope of a linear?
The slope of a linear function is also a measure of how fast the function is increasing or decreasing. The only difference is that the slope of a straight line remains the same throughout the domain of the line.
How do you determine the rate of change in a graph?
Rate of change is essentially the same as the slope of a graph, that is change in y divided by change in x. If the graph is a straight-line, the slope can be easily calculated with the formula:Vertical change ÷ horizontal change = (y2 - y1) / (x2 - x1)
What is an example of constant rate of change?
A constant rate of change is anything that increases or decreases by the same amount for every trial. Therefore an example could be driving down the highway at a speed of exactly 60 MPH. If your speed doesn't change you are driving at a constant rate. Here's another: your cell phone company charges you $0.55 for every minute you use. The rate that you are charged always stays the same so it is a constant rate of change. Anything that goes up by X number of units for every Y value every time is a constant rate of change.
What is the rate of change between any two points on a line?
it is the same as the slope, which can be found either graphically (rise over run) or algebraically using the formula (y2-y1)/(x2-x1)
