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Q: Slope measures the of the y-variable with respect to the x-variable?
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The slope of a line measures what?

The slope of a line measures the steepness of the line.


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.


What instrument measures slope?

Protractor or bevel gauge.


What measures acceleration on a speed-time graph?

The slope.


What does a clinometer measure?

It measures angle of a slope or tilt


What is the slope of horizontal line?

The slope of a horizontal line is zero. That's because the slope measures how steep the line is, and a flat line is not steep at all and therefore has no slope.


What part of a line that is also called rise-over-run measures the steepness?

It is the slope or gradient of the line that measures its steepness.


What is the line of regression?

line that measures the slope between dependent and independent variables


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 under the curve of a displacement versus time reveal?

There is no such thing as a "slope under the curve", so I assume that you mean "slope of the curve". If the curve is d vs. t, where d is displacement and t is time, then the slope at any given point will yield (reveal) the velocity, since velocity is defined as the rate of change of distance with respect to time. Mathematically speaking, velocity is the first derivative of position with respect to time. The second derivative - change in velocity with respect to time - is acceleration.


Why does a constant speed have a slope of 0?

Because the slope measures the rate of change. The word "CONSTANT" means no change so there is no rate of change. Having said that, it will not have a slope of zero if you are plotting displacement against time.


On speed-time graph the measures acceleration?

On speed-time graph can measure acceleration by getting the slope.