Question
Give the slope and y-intercept of the line whose equation is given. Then graph the linear function.
f(x)equalsminustwo thirds
xplus5
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The slope is
enter your response here.
(Simplify your answer. Type an integer or a fraction.)
B.
The slope is undefined.
f(x)equalsminustwo thirds
xplus5
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The slope is
enter your response here.
(Simplify your answer. Type an integer or a fraction.)
B.
The slope is undefined.
Answers
GPT-4o mini
The given equation of the line is \( f(x) = -\frac{2}{3}x + 5 \).
### Part 1
A. To identify the slope and y-intercept from the equation \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:
- **Slope (m)**: The coefficient of \( x \) is \( -\frac{2}{3} \).
- **y-Intercept (b)**: The constant term is \( 5 \).
Thus, the slope is \( -\frac{2}{3} \), and the y-intercept is \( 5 \).
So, the answer is:
- The slope is \(-\frac{2}{3}\).
### Part 2: Graphing the Function
1. **Plot the y-intercept**: Start by plotting the point \( (0, 5) \) on the graph.
2. **Use the slope to find another point**: From the y-intercept, use the slope \( -\frac{2}{3} \) which means for every 3 units you move to the right (positive x-direction), you move 2 units down (negative y-direction).
- From \( (0, 5) \), moving 3 units right to \( (3, 5) \) and then moving down 2 units to \( (3, 3) \), we get another point.
3. **Plot the second point**: Plot \( (3, 3) \).
4. **Draw the line**: Draw a straight line through the points \( (0, 5) \) and \( (3, 3) \).
The graph of the function would show a downward sloping line passing through those points. Here is a rough description of the graphing steps:
- Start at \( (0, 5) \).
- Move to \( (3, 3) \).
- Connect these points with a straight line extending in both directions.
The overall graph represents the linear function \( f(x) = -\frac{2}{3}x + 5 \).
### Part 1
A. To identify the slope and y-intercept from the equation \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:
- **Slope (m)**: The coefficient of \( x \) is \( -\frac{2}{3} \).
- **y-Intercept (b)**: The constant term is \( 5 \).
Thus, the slope is \( -\frac{2}{3} \), and the y-intercept is \( 5 \).
So, the answer is:
- The slope is \(-\frac{2}{3}\).
### Part 2: Graphing the Function
1. **Plot the y-intercept**: Start by plotting the point \( (0, 5) \) on the graph.
2. **Use the slope to find another point**: From the y-intercept, use the slope \( -\frac{2}{3} \) which means for every 3 units you move to the right (positive x-direction), you move 2 units down (negative y-direction).
- From \( (0, 5) \), moving 3 units right to \( (3, 5) \) and then moving down 2 units to \( (3, 3) \), we get another point.
3. **Plot the second point**: Plot \( (3, 3) \).
4. **Draw the line**: Draw a straight line through the points \( (0, 5) \) and \( (3, 3) \).
The graph of the function would show a downward sloping line passing through those points. Here is a rough description of the graphing steps:
- Start at \( (0, 5) \).
- Move to \( (3, 3) \).
- Connect these points with a straight line extending in both directions.
The overall graph represents the linear function \( f(x) = -\frac{2}{3}x + 5 \).