Math / Algebra

QuestionA linear function is given. Complete parts (a)-(d). $h(x)=\frac{1}{2} x-6$
The slope is $\frac{1}{2}$ . (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 $\frac{1}{2}$ . (Type an integer or a fraction.) (d) Determine whether the linear function is increasing, decreasing, or constant. Choose the correct answer below. A. decreasing B. constant C. increasing

Studdy Solution

STEP 1

1. The function given is a linear function of the form $h(x) = mx + b$ .
2. The slope $m$ of a linear function determines its rate of change and whether it is increasing or decreasing.
3. The $y$ -intercept $b$ is the point where the line crosses the $y$ -axis.
4. The average rate of change for a linear function is constant and equal to the slope.

STEP 2

1. Identify the slope and $y$ -intercept from the function.
2. Use the slope and $y$ -intercept to graph the function.
3. Determine the average rate of change.
4. Determine whether the function is increasing, decreasing, or constant.

STEP 3

Identify the slope and $y$ -intercept from the function $h(x) = \frac{1}{2}x - 6$ .
- The slope $m$ is the coefficient of $x$ , which is $\frac{1}{2}$ . - The $y$ -intercept $b$ is the constant term, which is $-6$ .

STEP 4

To graph the function, start by plotting the $y$ -intercept on the graph:
- Plot the point $(0, -6)$ on the $y$ -axis.
Next, use the slope to find another point:
- The slope $\frac{1}{2}$ means that for every 2 units you move to the right (positive $x$ -direction), you move 1 unit up (positive $y$ -direction). - From the point $(0, -6)$ , move 2 units to the right to $(2, -6)$ and 1 unit up to $(2, -5)$ . - Plot the point $(2, -5)$ .
Draw a line through the points $(0, -6)$ and $(2, -5)$ .

STEP 5

Determine the average rate of change of the function:
- For a linear function, the average rate of change is equal to the slope. - Therefore, the average rate of change is $\frac{1}{2}$ .

STEP 6

Determine whether the linear function is increasing, decreasing, or constant:
- A positive slope indicates the function is increasing. - Since the slope $\frac{1}{2}$ is positive, the function is increasing.
The correct answer is: C. increasing

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Studdy Solution

STEP 1

STEP 2

1. Identify the slope and $y$ -intercept from the function.
2. Use the slope and $y$ -intercept to graph the function.
3. Determine the average rate of change.
4. Determine whether the function is increasing, decreasing, or constant.

STEP 3

Identify the slope and $y$ -intercept from the function $h(x) = \frac{1}{2}x - 6$ .
- The slope $m$ is the coefficient of $x$ , which is $\frac{1}{2}$ . - The $y$ -intercept $b$ is the constant term, which is $-6$ .

STEP 4

STEP 5

Determine the average rate of change of the function:
- For a linear function, the average rate of change is equal to the slope. - Therefore, the average rate of change is $\frac{1}{2}$ .

STEP 6

Determine whether the linear function is increasing, decreasing, or constant:
- A positive slope indicates the function is increasing. - Since the slope $\frac{1}{2}$ is positive, the function is increasing.
The correct answer is: C. increasing

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Studdy Solution

STEP 1

STEP 2

1. Identify the slope and y y y-intercept from the function.2. Use the slope and y y y-intercept to graph the function.3. Determine the average rate of change.4. Determine whether the function is increasing, decreasing, or constant.

STEP 3

Identify the slope and y y y-intercept from the function h(x)=12x−6 h(x) = \frac{1}{2}x - 6 h(x)=21​x−6.- The slope m m m is the coefficient of x x x, which is 12 \frac{1}{2} 21​. - The y y y-intercept b b b is the constant term, which is −6-6−6.

STEP 4

STEP 5

Determine the average rate of change of the function:- For a linear function, the average rate of change is equal to the slope. - Therefore, the average rate of change is 12 \frac{1}{2} 21​.

STEP 6

Determine whether the linear function is increasing, decreasing, or constant:- A positive slope indicates the function is increasing. - Since the slope 12 \frac{1}{2} 21​ is positive, the function is increasing.The correct answer is: C. increasing

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1. Identify the slope and $y$ -intercept from the function.
2. Use the slope and $y$ -intercept to graph the function.
3. Determine the average rate of change.
4. Determine whether the function is increasing, decreasing, or constant.

Identify the slope and $y$ -intercept from the function $h(x) = \frac{1}{2}x - 6$ .
- The slope $m$ is the coefficient of $x$ , which is $\frac{1}{2}$ . - The $y$ -intercept $b$ is the constant term, which is $-6$ .

Determine the average rate of change of the function:
- For a linear function, the average rate of change is equal to the slope. - Therefore, the average rate of change is $\frac{1}{2}$ .

Determine whether the linear function is increasing, decreasing, or constant:
- A positive slope indicates the function is increasing. - Since the slope $\frac{1}{2}$ is positive, the function is increasing.
The correct answer is: C. increasing