Question
Which description of the graph of the linear inequality y ≥ 7x – 4 is correct?
The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
Answers
GPT-4o mini
To analyze the linear inequality \( y \geq 7x - 4 \), let's break down its components:
1. **Line Representation**: The related equation is \( y = 7x - 4 \).
- **Y-Intercept**: This is the point where the line crosses the y-axis, which occurs when \( x = 0 \). Plugging in \( x = 0 \):
\[
y = 7(0) - 4 = -4
\]
So the y-intercept is \( -4 \).
- **Slope**: The slope of the line is the coefficient of \( x \), which is \( 7 \).
2. **Solid vs. Dashed Line**:
- The inequality sign \( \geq \) indicates that the line should be **solid** (because points on the line itself satisfy the inequality).
3. **Shading Direction**:
- Since the inequality is \( y \geq 7x - 4 \), we will shade **above** the line. This represents all the points where the \( y \)-value is greater than or equal to the linear expression on the right.
With this information established, the correct description of the graph is:
**The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.**
1. **Line Representation**: The related equation is \( y = 7x - 4 \).
- **Y-Intercept**: This is the point where the line crosses the y-axis, which occurs when \( x = 0 \). Plugging in \( x = 0 \):
\[
y = 7(0) - 4 = -4
\]
So the y-intercept is \( -4 \).
- **Slope**: The slope of the line is the coefficient of \( x \), which is \( 7 \).
2. **Solid vs. Dashed Line**:
- The inequality sign \( \geq \) indicates that the line should be **solid** (because points on the line itself satisfy the inequality).
3. **Shading Direction**:
- Since the inequality is \( y \geq 7x - 4 \), we will shade **above** the line. This represents all the points where the \( y \)-value is greater than or equal to the linear expression on the right.
With this information established, the correct description of the graph is:
**The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.**