Graph the linear inequality shown below on the provided graph. y ≤ (1/3)x - 6.
Understand the Problem
The question is instructing the user to graph a linear inequality, specifically y ≤ (1/3)x - 6, on a provided graph. The task involves using drawing tools to represent the inequality accurately on the graph.
Answer
Draw a solid line through (0, -6) and (3, -5), and shade below the line.
Answer for screen readers
The correct representation involves plotting a solid line through points (0, -6) and (3, -5), then shading the area below the line.
Steps to Solve
- Identify the boundary line equation
The given inequality is $y \leq \frac{1}{3}x - 6$. We can think of the boundary line based on the equation $y = \frac{1}{3}x - 6$.
- Find the slope and y-intercept
The slope (m) is $\frac{1}{3}$ and the y-intercept (b) is -6. This means the line crosses the y-axis at (0, -6).
- Plot the y-intercept
On the graph, locate the point (0, -6) and place a point there.
- Use the slope to find a second point
From (0, -6), use the slope $\frac{1}{3}$ to find another point:
- Move up 1 unit and right 3 units from (0, -6). This leads to the point (3, -5).
- Draw the boundary line
Since the inequality is $y \leq \frac{1}{3}x - 6$, you will draw a solid line through the points (0, -6) and (3, -5). A solid line indicates that points on the line are included in the solution.
- Shade the appropriate region
Since the inequality states $y \leq \frac{1}{3}x - 6$, shade the region below the line to represent all the points where $y$ is less than or equal to the value of the line.
The correct representation involves plotting a solid line through points (0, -6) and (3, -5), then shading the area below the line.
More Information
This linear inequality represents a region of solutions in the coordinate plane where all points satisfy the condition of the inequality. The inclusion of the line indicates that points on the line itself are valid solutions.
Tips
- Forgetting to use a solid line instead of a dashed line for $\leq$ and $\geq$ inequalities.
- Incorrectly shading the area above the line instead of below it for inequalities involving $\leq$.
AI-generated content may contain errors. Please verify critical information
