Question
Graph the inequality y is less than or equal to 4x +2
Answers
GPT-4o mini
To graph the inequality \( y \leq 4x + 2 \), follow these steps:
1. **Graph the boundary line**: First, we need to graph the equation \( y = 4x + 2 \).
- This is a linear equation in slope-intercept form \( y = mx + b \), where \( m = 4 \) (the slope) and \( b = 2 \) (the y-intercept).
- To plot the line, start by placing a point at the y-intercept (0, 2) on the y-axis.
- From this point, use the slope to find another point: from (0, 2), go up 4 units and to the right 1 unit to get to (1, 6).
- Connect these points with a straight line.
2. **Determine the type of line**: Since the inequality is "less than or equal to" (\( \leq \)), we will draw the line solid to indicate that points on the line are included in the solution set.
3. **Shade the appropriate region**:
- Since the inequality is \( y \leq 4x + 2 \), we need to shade the region below the line. This represents all the points (x, y) where the y-coordinate is less than or equal to \( 4x + 2 \).
4. **Final graph**: The final graph consists of a solid line representing \( y = 4x + 2 \) and the area beneath the line shaded.
If you want a visual representation, you can sketch this on graph paper or use graphing software to plot the line and shade the appropriate region.
1. **Graph the boundary line**: First, we need to graph the equation \( y = 4x + 2 \).
- This is a linear equation in slope-intercept form \( y = mx + b \), where \( m = 4 \) (the slope) and \( b = 2 \) (the y-intercept).
- To plot the line, start by placing a point at the y-intercept (0, 2) on the y-axis.
- From this point, use the slope to find another point: from (0, 2), go up 4 units and to the right 1 unit to get to (1, 6).
- Connect these points with a straight line.
2. **Determine the type of line**: Since the inequality is "less than or equal to" (\( \leq \)), we will draw the line solid to indicate that points on the line are included in the solution set.
3. **Shade the appropriate region**:
- Since the inequality is \( y \leq 4x + 2 \), we need to shade the region below the line. This represents all the points (x, y) where the y-coordinate is less than or equal to \( 4x + 2 \).
4. **Final graph**: The final graph consists of a solid line representing \( y = 4x + 2 \) and the area beneath the line shaded.
If you want a visual representation, you can sketch this on graph paper or use graphing software to plot the line and shade the appropriate region.