Questions: A linear function is given. Complete parts (a) (d). g(x)=2x+6 (a) Determine the slope and y-intercept of the function. The slope is 2. (Type an integer or a simplified fraction.) The y-intercept is 6 (Type an integer or a simplified fraction.) (b) Use the slope and y-intercept to graph the linear function. Use the graphing tool to graph the function. Use the slope and y-intercept when drawing the line. (c) Determine the average rate of change of the function. The average rate of change is 2. (d) Determine whether the linear function is increasing, decreasing, or constant Choose the correct answer below. A. constant B. increasing C. decreasing

A linear function is given. Complete parts (a) (d). g(x)=2x+6 (a) Determine the slope and y-intercept of the function. The slope is 2. (Type an integer or a simplified fraction.) The y-intercept is 6 (Type an integer or a simplified fraction.) (b) Use the slope and y-intercept to graph the linear function. Use the graphing tool to graph the function. Use the slope and y-intercept when drawing the line. (c) Determine the average rate of change of the function. The average rate of change is 2. (d) Determine whether the linear function is increasing, decreasing, or constant Choose the correct answer below. A. constant B. increasing C. decreasing
Transcript text: A linear function is given. Complete parts (a) (d). \[ g(x)=2 x+6 \] (a) Determine the slope and $y$-intercept of the function. The slope is 2 . (Type an integer or a simplified fraction.) The $y$-intercept is 6 (Type an integer or a simplified fraction.) (b) Use the slope and $y$-intercept to graph the linear function. Use the graphing tool to graph the function. Use the slope and $y$-intercept when drawing the line. $\square$ (c) Determine the average rate of change of the function. The average rate of change is 2 . (d) Determine whether the linear function is increasing, decreasing, or constant Choose the correct answer below. A. constant B. increasing C. decreasing
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Solution

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Solution Steps

Step 1: Determine the slope and y-intercept

The given linear function is: \[ g(x) = 2x + 6 \] The slope is \(2\) and the \(y\)-intercept is \(6\).

Step 2: Graph the linear function

We will use the slope and \(y\)-intercept to graph the function.

Step 3: Determine the average rate of change

For a linear function, the average rate of change is equal to the slope. Therefore, the average rate of change is \(2\).

Final Answer

The slope is \(2\) and the \(y\)-intercept is \(6\). The average rate of change is \(2\).

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