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Yes, Rate of change is slope
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∙ 9y ago
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Do all lines have a slope?
Although all lines have the relationship that defines slope, one can argue that not all lines do have one. The exception would be vertical lines. Slope is defined as the vertical rate of change divided by the horizontal rate of change. In the case of a vertical line, there is no horizontal rate of change, and calculating slope would cause division by zero. The closest you could come to expressing the slope of a vertical line would be ∞
Does in linear graphs the slope of the line change with the x-coordinate?
No. A linear graph has the same slope anywhere.
If one line has a slope of then the slope of a line parallel to it would be?
The same. Parallel lines have the same slope.
What does the slope of the line represent?
The slope represents the RATE OF CHANGE. Example: the distance (y) over speed (x) the formula is rise÷run or y2-y1÷x2-x1= m Slope is represented as m in the equations y=mx+b and y=mx
How can the slope of a line be used to describe a line?
The slope is just the rate of change. For every change along the x-axis, the y-axis changes.y = mx + b, where m is the slope and b is just an arbitrary constant. Because of this, let's just assume b is equal to 0.So, if m = 4:y = 4x + 0y = 4xIn this case, y is always 4 times larger than what x is equal to, except when x is equal to zero (because they are both equal to zero in that case).If x is equal to 2:y = 4(2) = 8, so you can clearly see y is 4 times larger than x.Slope, or rate of change, represents: change in y divided by change in x (or more commonly, "rise over run")So the answer here, is slope can describe the rate of change of a line.
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.
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.
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 difference between rate of change and slope?
Slope is blah. Rate of change is blah.
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 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 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.
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)
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
