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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 do you know if a function has a constant or variable rate of change?
If the graph is a non-vertical straight line, then the rate of change is constant. If the line is curved, then the rate of change (slope) varies.
What does the slope of a line tell you on a graph?
the rate of change on the 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.
The constant rate of change between two points on a line?
The constant rate of change between two points on a line is called slope.
Is the following function linear or nonlinear If linear, state the rate of change?
o function is given. However, if linear , then the rate of change is the same as the steepness of the graph 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
An important property of every line is its steepness or?
slope, which indicates how steeply the line rises or falls as it moves along its path. The slope is found by taking the ratio of the vertical change to the horizontal change between two points on the line. It is a measure of the rate at which the line is ascending or descending.
Another name for slope?
Gradient is another term used to describe the slope of a line or surface. It represents the rate of change or steepness of a line or surface.
What does the steepness of the slope tell you about the speed of an object?
The steepness of the slope indicates the rate at which the object's speed is changing. A steeper slope suggests a faster change in speed, while a shallower slope indicates a slower change in speed.
Is the rate of change for a vertical line 0?
no. the rate of change is undefined.
What does the steepness or slope of a graph indicate?
The steepness or slope of a graph indicates the rate of change or gradient of the function being represented. A steeper slope indicates a faster rate of change, while a shallower slope indicates a slower rate of change.
How do you know if a function has a constant or variable rate of change?
If the graph is a non-vertical straight line, then the rate of change is constant. If the line is curved, then the rate of change (slope) varies.
What does the slope of a line tell you on a graph?
the rate of change on the 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.
The constant rate of change between two points on a line?
The constant rate of change between two points on a line is called slope.
Does a steep curve on a line graph indicate rapid or a slow rate of change?
A rapid rate of change (which looks like this, U). A slow rate of change would have a slowly declining line like this (\ \ \ )
