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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
What is the relationship among proportional relationship lines rate of change and slope?
The rate of change is the same as the slope.
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 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
How can slope relate to pythagorean theorem?
It does not relate to it
Is rate of change the same as slope?
Yes, Rate of change is slope
What is the difference between a slope and rate of change?
Depends. Slope of tangent = instantaneous rate of change. Slope of secant = average rate of change.
How can snowboarding relate to geometry?
slope of the hill
What is the difference between rate of change and slope?
Slope is blah. Rate of change is blah.
How does slope and distance relate to transformation?
In general, they don't.
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
What is the relationship among proportional relationship lines rate of change and slope?
The rate of change is the same as the slope.
What is another name for rate of change?
slope of a line
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 does the slope of an acceleration time graph indicate?
The slope of an acceleration-time graph represents the rate of change of acceleration over time. A steeper slope indicates a faster rate of acceleration, while a less steep slope indicates a slower rate of acceleration.
Why is the slope called the rate of change?
On a graph, the slope does tell you the rate of change of y with respect to x. If the slope is steep, that means that there is a high rate of change of y with respect to x. If the slope is shallow, then y is not changing that rapidly with respect to x.
