Question
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Part 1
Sketch a graph of yequalsf(x).
f(x)equalsone half
xplus3
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Part 1
Use the graphing tool to graph the line.
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Part 1
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Answers
Answered by
GPT-4o mini
To sketch the graph of the function \( f(x) = \frac{1}{2}x + 3 \), follow these steps:
1. **Identify the Slope and Y-Intercept**:
- The function is in the slope-intercept form \( y = mx + b \).
- Here, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( b \) is \( 3 \).
2. **Plot the Y-Intercept**:
- Start by plotting the y-intercept at the point \( (0, 3) \).
3. **Use the Slope**:
- The slope \( \frac{1}{2} \) means that for every 1 unit you go up (rise), you move 2 units to the right (run).
- From the point \( (0, 3) \), move up 1 unit to \( (0, 4) \) and then move 2 units to the right to \( (2, 4) \). Plot this point.
4. **Draw the Line**:
- Draw a straight line through the two points plotted: \( (0, 3) \) and \( (2, 4) \).
- Extend the line in both directions.
5. **Label the Axes**:
- Make sure to label your x-axis and y-axis.
6. **Additional Points (Optional)**:
- For a more accurate graph, you can find more points by substituting values for \( x \) into the function:
- For example, if \( x = -2 \):
\[
f(-2) = \frac{1}{2}(-2) + 3 = -1 + 3 = 2 \quad \Rightarrow \quad (-2, 2)
\]
- If \( x = 2 \):
\[
f(2) = \frac{1}{2}(2) + 3 = 1 + 3 = 4 \quad \Rightarrow \quad (2, 4)
\]
7. **Final Graph**:
- Once you have your points plotted, you will have a linear graph that increases steadily from left to right, starting higher at \( y = 3 \) when \( x = 0 \) and continuing to rise as \( x \) increases.
### Summary
- The graph of \( f(x) = \frac{1}{2}x + 3 \) is a straight line that has a y-intercept at \( (0, 3) \) and goes up 1 unit for every 2 units it moves to the right.
Please refer to graphing software or tools to input the function directly for precise graphical representation. If you are using grid paper or a digital graphing tool, you can plot these points and draw the line as described!
1. **Identify the Slope and Y-Intercept**:
- The function is in the slope-intercept form \( y = mx + b \).
- Here, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( b \) is \( 3 \).
2. **Plot the Y-Intercept**:
- Start by plotting the y-intercept at the point \( (0, 3) \).
3. **Use the Slope**:
- The slope \( \frac{1}{2} \) means that for every 1 unit you go up (rise), you move 2 units to the right (run).
- From the point \( (0, 3) \), move up 1 unit to \( (0, 4) \) and then move 2 units to the right to \( (2, 4) \). Plot this point.
4. **Draw the Line**:
- Draw a straight line through the two points plotted: \( (0, 3) \) and \( (2, 4) \).
- Extend the line in both directions.
5. **Label the Axes**:
- Make sure to label your x-axis and y-axis.
6. **Additional Points (Optional)**:
- For a more accurate graph, you can find more points by substituting values for \( x \) into the function:
- For example, if \( x = -2 \):
\[
f(-2) = \frac{1}{2}(-2) + 3 = -1 + 3 = 2 \quad \Rightarrow \quad (-2, 2)
\]
- If \( x = 2 \):
\[
f(2) = \frac{1}{2}(2) + 3 = 1 + 3 = 4 \quad \Rightarrow \quad (2, 4)
\]
7. **Final Graph**:
- Once you have your points plotted, you will have a linear graph that increases steadily from left to right, starting higher at \( y = 3 \) when \( x = 0 \) and continuing to rise as \( x \) increases.
### Summary
- The graph of \( f(x) = \frac{1}{2}x + 3 \) is a straight line that has a y-intercept at \( (0, 3) \) and goes up 1 unit for every 2 units it moves to the right.
Please refer to graphing software or tools to input the function directly for precise graphical representation. If you are using grid paper or a digital graphing tool, you can plot these points and draw the line as described!