This question is based on the concept of equation of line. Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.
We need to determined the the rate of change of y with respect to x for this function.
According to the question,
A linear relationship of line can be written as:
y = a [tex]\bold{\times}[/tex] x + b
Where, a is the slope ( rate of change of y with respect to x) and b is the y-axis intercept.
For a line that passes through the points[tex]\bold{(x_1, y_1) }[/tex] and [tex]\bold{(x_2, y_2)}[/tex]. Thus, the slope can be written as:
[tex]a = \dfrac{(y_2- y_1) }{(x_2 - x_1)}[/tex]
It is given that, the points are (-3, 3.6) and (5, 2)
. Then the slope will be:
[tex]\bold{a = \dfrac{(2- 3.6) }{( 5- (-3) )} = \dfrac{-1.6}{8} = -0.2}[/tex]
Then the rate of change is -0.2.
Now, the equation of line become,
y = -0.2 x + b
Now, find the value of b, we can simply replace the values of one of the points in that equation, use the point (5, 2)
.This means that we must replace x by 5, and y by 2.
2 = -0.2*5 + b
2 = -1 + b
2 + 1 = b
3 = b
Then the equation is: y = -0.2 x + 3.
Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.
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