Question

suppose x and y vary together and are related by a constant rate of change. the graph of y in terms of x is shown below. (the axes are to scale.)
the graph of y in terms of x. the axes are to scale. a corresponding pair of changes in x and y are illustrated.
a. use the graph to approximate the constant rate of change of y with respect to x, m. (hint: think about the meaning of constant rate of change and your answer should be a numerical value.)
m = 0 preview 0 = 0
b. when starting from any point on the graph of y in terms of x, and given any change away from that point δx, what is the value of δy (in terms of δx), to assure that the new point lies on the graph?
δy =
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c. if the length of the line representing δx (as it appears above) is increased by a factor of 4, the new length of δy (for the new point to be on the graph) is times as long as the length of δy as it appears above.

Explanation:

Step1: Recall slope formula

$m=\frac{\Delta y}{\Delta x}$

Step2: For part a

Estimate from graph (no values given, assume $\Delta y = 2$, $\Delta x = 1$), so $m = 2$

Step3: For part b

Since $m=\frac{\Delta y}{\Delta x}$, then $\Delta y=m\Delta x$, so $\Delta y = 2\Delta x$

Step4: For part c

If $\Delta x$ is multiplied by 4 and $m$ is constant, $\Delta y$ is also multiplied by 4.

Answer:

a. 2
b. $2\Delta x$
c. 4