Question
The phone with system of inequalities by graphing why is less than 10x - 4
Answers
Answered by
GPT-4o mini
To graph the system of inequalities involving a line defined by \( y < 10x - 4 \), we'll follow a series of steps:
1. **Graph the line \( y = 10x - 4 \)**:
- First, we find two points on the line.
- When \( x = 0 \):
\[
y = 10(0) - 4 = -4 \quad \text{(Point: (0, -4))}
\]
- When \( x = 1 \):
\[
y = 10(1) - 4 = 6 \quad \text{(Point: (1, 6))}
\]
2. **Plot the points**:
- Plot the points (0, -4) and (1, 6) on a Cartesian plane.
3. **Draw the line**:
- Since the inequality is \( y < 10x - 4 \), we will draw a dashed line (not solid) because the points on the line itself are not included in the solution.
4. **Shading the appropriate region**:
- Since \( y < 10x - 4 \), we shade the area below the dashed line, where all the points satisfy the inequality.
To summarize, the graph of the system will consist of:
- A dashed line through the points (0, -4) and (1, 6).
- Shading below this line to indicate all points (x, y) where \( y \) is less than \( 10x - 4 \).
If you have additional inequalities to include in the system, you would repeat the steps for each one and find the overlapping shaded region that satisfies all inequalities.
1. **Graph the line \( y = 10x - 4 \)**:
- First, we find two points on the line.
- When \( x = 0 \):
\[
y = 10(0) - 4 = -4 \quad \text{(Point: (0, -4))}
\]
- When \( x = 1 \):
\[
y = 10(1) - 4 = 6 \quad \text{(Point: (1, 6))}
\]
2. **Plot the points**:
- Plot the points (0, -4) and (1, 6) on a Cartesian plane.
3. **Draw the line**:
- Since the inequality is \( y < 10x - 4 \), we will draw a dashed line (not solid) because the points on the line itself are not included in the solution.
4. **Shading the appropriate region**:
- Since \( y < 10x - 4 \), we shade the area below the dashed line, where all the points satisfy the inequality.
To summarize, the graph of the system will consist of:
- A dashed line through the points (0, -4) and (1, 6).
- Shading below this line to indicate all points (x, y) where \( y \) is less than \( 10x - 4 \).
If you have additional inequalities to include in the system, you would repeat the steps for each one and find the overlapping shaded region that satisfies all inequalities.