Question
Graph the inequality on the axes below.
y, is greater than or equal to, start fraction, 3, divided by, 4, end fraction, x, minus, 4
y≥
4
3
x−4
y, is greater than or equal to, start fraction, 3, divided by, 4, end fraction, x, minus, 4
y≥
4
3
x−4
Answers
GPT-4o mini
To graph the inequality \( y \geq \frac{3}{4}x - 4 \), follow these steps:
1. **Find the Equation of the Line**: First, we start with the equation of the line corresponding to the inequality:
\[
y = \frac{3}{4}x - 4
\]
2. **Identify the Slope and Y-Intercept**: The slope \( m \) is \( \frac{3}{4} \) and the y-intercept \( b \) is \( -4 \). This tells you that the line will rise 3 units for every 4 units it runs to the right.
3. **Plot the Y-Intercept**: Start by plotting the y-intercept at the point \( (0, -4) \).
4. **Use the Slope to Plot Another Point**: From the y-intercept, use the slope to find another point. From \( (0, -4) \), moving right 4 units and up 3 units takes you to the point \( (4, -1) \). Plot this point as well.
5. **Draw the Line**: Since the inequality is \( \geq \), you will draw a solid line through these points to indicate that points on the line are included in the solution.
6. **Shade the Region**: Since the inequality is \( y \geq \), shade the region above the line. This represents all the points where the \( y \)-values are greater than or equal to the line.
7. **Indicate the Axes**: Ensure you have both the x-axis and y-axis shown on your graph.
Here is how the graph looks in summary:
- Draw a solid line through the points \( (0, -4) \) and \( (4, -1) \).
- Shade the area above this line.
If you have graphing software or graph paper, plot these points and follow through the steps to get your final graph!
1. **Find the Equation of the Line**: First, we start with the equation of the line corresponding to the inequality:
\[
y = \frac{3}{4}x - 4
\]
2. **Identify the Slope and Y-Intercept**: The slope \( m \) is \( \frac{3}{4} \) and the y-intercept \( b \) is \( -4 \). This tells you that the line will rise 3 units for every 4 units it runs to the right.
3. **Plot the Y-Intercept**: Start by plotting the y-intercept at the point \( (0, -4) \).
4. **Use the Slope to Plot Another Point**: From the y-intercept, use the slope to find another point. From \( (0, -4) \), moving right 4 units and up 3 units takes you to the point \( (4, -1) \). Plot this point as well.
5. **Draw the Line**: Since the inequality is \( \geq \), you will draw a solid line through these points to indicate that points on the line are included in the solution.
6. **Shade the Region**: Since the inequality is \( y \geq \), shade the region above the line. This represents all the points where the \( y \)-values are greater than or equal to the line.
7. **Indicate the Axes**: Ensure you have both the x-axis and y-axis shown on your graph.
Here is how the graph looks in summary:
- Draw a solid line through the points \( (0, -4) \) and \( (4, -1) \).
- Shade the area above this line.
If you have graphing software or graph paper, plot these points and follow through the steps to get your final graph!