Find the average rate of change of $$ g(x)=-2 x+1 $$ between the points $$ (-4,9) $$ and $$ (2,-3) $$

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UpStudy AI · Accepted Answer

**Step 1:**  
The formula for the average rate of change of a function $$ g(x) $$ between two points $$ (x_1, g(x_1)) $$ and $$ (x_2, g(x_2)) $$ is given by  
$$
\text{Average Rate of Change} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}.
$$

**Step 2:**  
Given the points $$ (-4,9) $$ and $$ (2,-3) $$, we have:  
$$
x_1 = -4,\quad g(x_1) = 9,\quad x_2 = 2,\quad g(x_2) = -3.
$$

**Step 3:**  
Substitute these values into the formula:
$$
\text{Average Rate of Change} = \frac{-3 - 9}{2 - (-4)}.
$$

**Step 4:**  
Simplify the numerator and the denominator:
$$
-3 - 9 = -12,
$$
$$
2 - (-4) = 2 + 4 = 6.
$$

**Step 5:**  
Divide the numerator by the denominator:
$$
\frac{-12}{6} = -2.
$$

**Final Answer:**  
The average rate of change of $$ g(x)=-2x+1 $$ between the given points is $$-2$$.
The average rate of change is -2.

Find the average rate of change of between the points and

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