QuestionA linear function is given. Complete parts (a)-(d).
(a) Determine the slope and -intercept of the function.
The slope is 4 .
(Type an integer or a simplified fraction.)
The -intercept is 2 .
(Type an integer or a simplified fraction.)
(b) Use the slope and -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
Studdy Solution
STEP 1
1. The function is a linear function.
2. For linear functions, the slope-intercept form is , where is the slope and is the -intercept.
3. The average rate of change for a linear function is constant and equal to the slope.
STEP 2
1. Identify the slope and -intercept from the function.
2. Graph the linear function using the slope and -intercept.
3. Determine the average rate of change of the function.
STEP 3
Identify the slope and -intercept from the function .
The function is in the form , where:
- is the slope.
- is the -intercept.
For :
- The slope .
- The -intercept .
STEP 4
To graph the linear function, start by plotting the -intercept on the graph. The -intercept is the point where the line crosses the -axis.
1. Plot the point on the graph.
2. Use the slope to determine another point. The slope can be interpreted as "rise over run," meaning for every 1 unit you move to the right (positive -direction), you move 4 units up (positive -direction).
3. From the point , move 1 unit to the right to and 4 units up to . Plot the point .
4. Draw a straight line through the points and .
STEP 5
Determine the average rate of change of the function.
For a linear function, the average rate of change between any two points is constant and equal to the slope of the line.
Thus, the average rate of change of the function is equal to the slope, which is .
The average rate of change is .
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