Provide a 150 word response to the following questions.
Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours.
What does the slope of this line represent? How is this graph useful?
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A Cartesian plane whose x-axis represents the number of hours a person walks while the y-axis represents the distance travelled by the person can be used to examine a lot of things related to the motion of the person. For instance, by simply looking at the x-coordinate, one can immediately tell, by looking at the corresponding y-value of the line at the given x-coordinate, the distance travelled at time x hours.
Getting the slope, on the other hand, would reveal to us the speed of the person. Slope is, generally, given by the formula `m = (y_2 - y_1)/(x_2 - x_1) = (Delta y)/(Delta x)` . Delta here denotes change, and we see that the slope is simply the change in the distance travelled for every given change in the number of hours - or the amount of travelled after a span of time - in other words, speed (Note the units: distance per time can be meters per second or kilometers per hour, of course, depending on the units of the values in your y- and x-axes.)
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