Question
Graph the inequality on the axes below.
y, is less than, minus, one quarter, x, plus, 1
y<−
4
1
x+1
y, is less than, minus, one quarter, x, plus, 1
y<−
4
1
x+1
Answers
GPT-4o mini
To graph the inequality \( y < -\frac{1}{4}x + 1 \), follow these steps:
1. **Graph the Boundary Line**:
The boundary of the inequality is the line given by the equation \( y = -\frac{1}{4}x + 1 \). This line should be dashed because the inequality is strict (it does not include the equality).
- **Find the y-intercept**: Set \( x = 0 \):
\[
y = -\frac{1}{4}(0) + 1 = 1
\]
The y-intercept is at the point \( (0, 1) \).
- **Find another point on the line**: Choose another value for \( x \). Let’s use \( x = 4 \):
\[
y = -\frac{1}{4}(4) + 1 = -1
\]
This gives us the point \( (4, -1) \).
- Now, plot the points \( (0, 1) \) and \( (4, -1) \) on the graph, then draw a dashed line through these points.
2. **Shade the Region**:
Since the inequality is \( y < -\frac{1}{4}x + 1 \), we need to shade below the line \( y = -\frac{1}{4}x + 1 \). This represents all the points where the y-value is less than the value given by the line.
3. **Final Graph**:
- Dashed line passing through \( (0, 1) \) and \( (4, -1) \).
- Shade the area below the line.
This completes the graph of the inequality \( y < -\frac{1}{4}x + 1 \).
If you're generating this graph digitally or on paper, make sure that your line is dashed with the correct shading indicating the solution set.
1. **Graph the Boundary Line**:
The boundary of the inequality is the line given by the equation \( y = -\frac{1}{4}x + 1 \). This line should be dashed because the inequality is strict (it does not include the equality).
- **Find the y-intercept**: Set \( x = 0 \):
\[
y = -\frac{1}{4}(0) + 1 = 1
\]
The y-intercept is at the point \( (0, 1) \).
- **Find another point on the line**: Choose another value for \( x \). Let’s use \( x = 4 \):
\[
y = -\frac{1}{4}(4) + 1 = -1
\]
This gives us the point \( (4, -1) \).
- Now, plot the points \( (0, 1) \) and \( (4, -1) \) on the graph, then draw a dashed line through these points.
2. **Shade the Region**:
Since the inequality is \( y < -\frac{1}{4}x + 1 \), we need to shade below the line \( y = -\frac{1}{4}x + 1 \). This represents all the points where the y-value is less than the value given by the line.
3. **Final Graph**:
- Dashed line passing through \( (0, 1) \) and \( (4, -1) \).
- Shade the area below the line.
This completes the graph of the inequality \( y < -\frac{1}{4}x + 1 \).
If you're generating this graph digitally or on paper, make sure that your line is dashed with the correct shading indicating the solution set.