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Assuming the variables are x (horizontal) and y (vertical), the slope of a straight line is defined as "rise over run". That is, the change in y divided by a change in x. This is exactly what the rate of change in y with respect to x, is.
If the line is a curve, the instantaneous slope is defined as the gradient of the tangent to the curve and is the limiting value (as dx tends to 0) of the same measure.
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Why can't a vertical line be used to represent rate of change?
the rate of change is related to the slope; the higher the slope, the higher the rate. If the line is vertical, that is infinite slope or infinite rate of change which is not possible
How is the steepness of the line is related to the rate of change?
the steepness of the line is the slope of the line which is the rate of change; the steeper the slope, the faster the rate of change
What does a slope of a line tell you?
The rate of change
What is the rate of change of a line called?
slope
What does the slope of a line tell you on a graph?
the rate of change on the line.
Why can't a vertical line be used to represent rate of change?
the rate of change is related to the slope; the higher the slope, the higher the rate. If the line is vertical, that is infinite slope or infinite rate of change which is not possible
How does the slope of a line represent a rate of change?
well the rate of change is how much something changes in a matter of time, so it can be graphed in a slope because slopes can represent changes ( negative and positive, zero and undefined)
How is the steepness of the line is related to the rate of change?
the steepness of the line is the slope of the line which is the rate of change; the steeper the slope, the faster the rate of change
When finding the slope of the trend line what does the slope mean about the data of the scatterplot?
The slope of the trend line is the rate of change of the data. It is the ratio of the change of the dependent variable to the rate of change of the independent variable. Slope represents the value of the correlation.
What is another name for rate of change?
slope of a line
What does a slope of a line tell you?
The rate of change
What is the rate of change of a line called?
slope
What does the slope of a line tell you on a graph?
the rate of change on the line.
What function does the slope of a line model?
rate of change
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 do you tell whether a graph shows a constant or variable rate of change?
The slope of each point on the line on the graph is the rate of change at that point. If the graph is a straight line, then its slope is constant. If the graph is a curved line, then its slope changes.
What does the slope of the curve on a velocity time graph represent?
The rate of Change in acceleration.
