Question
Where do you plot the points for y > 2/5x + 1
Answers
Answered by
GPT-4o mini
To plot the points for the inequality \( y > \frac{2}{5}x + 1 \), follow these steps:
1. **Graph the Line \( y = \frac{2}{5}x + 1 \)**:
- First, you need to graph the boundary line of the inequality. The equation \( y = \frac{2}{5}x + 1 \) is a straight line.
- To do this, find two points on the line:
- When \( x = 0 \):
\[
y = \frac{2}{5}(0) + 1 = 1 \quad \text{(Point (0, 1))}
\]
- When \( x = 5 \):
\[
y = \frac{2}{5}(5) + 1 = 3 \quad \text{(Point (5, 3))}
\]
- Plot these points: (0, 1) and (5, 3).
2. **Draw the Boundary Line**:
- Since the inequality is \( y > \frac{2}{5}x + 1 \), you will draw a dashed line (not solid) because the points on the line itself do not satisfy the inequality (the inequality does not include equality).
3. **Shade the Region**:
- The inequality \( y > \frac{2}{5}x + 1 \) indicates that you need to shade the area above the line. This represents all the points where \( y \) is greater than \( \frac{2}{5}x + 1 \).
4. **Choose Test Points**:
- You can verify which side of the line to shade by using a test point not on the line, such as (0, 0):
- Substitute \( (0, 0) \) into the inequality:
\[
0 > \frac{2}{5}(0) + 1 \quad \text{(This is false)}
\]
- Since the test point (0, 0) does not satisfy the inequality, you will shade the other side of the line.
In summary, plot the boundary line \( y = \frac{2}{5}x + 1 \) as a dashed line and shade the region above it to represent all points where \( y > \frac{2}{5}x + 1 \).
1. **Graph the Line \( y = \frac{2}{5}x + 1 \)**:
- First, you need to graph the boundary line of the inequality. The equation \( y = \frac{2}{5}x + 1 \) is a straight line.
- To do this, find two points on the line:
- When \( x = 0 \):
\[
y = \frac{2}{5}(0) + 1 = 1 \quad \text{(Point (0, 1))}
\]
- When \( x = 5 \):
\[
y = \frac{2}{5}(5) + 1 = 3 \quad \text{(Point (5, 3))}
\]
- Plot these points: (0, 1) and (5, 3).
2. **Draw the Boundary Line**:
- Since the inequality is \( y > \frac{2}{5}x + 1 \), you will draw a dashed line (not solid) because the points on the line itself do not satisfy the inequality (the inequality does not include equality).
3. **Shade the Region**:
- The inequality \( y > \frac{2}{5}x + 1 \) indicates that you need to shade the area above the line. This represents all the points where \( y \) is greater than \( \frac{2}{5}x + 1 \).
4. **Choose Test Points**:
- You can verify which side of the line to shade by using a test point not on the line, such as (0, 0):
- Substitute \( (0, 0) \) into the inequality:
\[
0 > \frac{2}{5}(0) + 1 \quad \text{(This is false)}
\]
- Since the test point (0, 0) does not satisfy the inequality, you will shade the other side of the line.
In summary, plot the boundary line \( y = \frac{2}{5}x + 1 \) as a dashed line and shade the region above it to represent all points where \( y > \frac{2}{5}x + 1 \).