Enter your answer and show all the steps that you use to solve this problem in the space provided. Write an inequality for the graph.
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To write an inequality for a graph, we need to first determine the inequality symbol based on the shading of the graph.
Step 1: Analyze the graph and note the shading:
Look at the graph and determine whether the shaded region is above or below the line.
Step 2: Identify the line on the graph:
Determine the equation of the line that represents the boundary of the shaded region. For example, if the line is y = 2x + 3, we will use this equation to form our inequality.
Step 3: Determine the inequality symbol:
Based on the shading:
- If the shaded region is below the line (including the line itself), we use "≤" or "<".
- If the shaded region is above the line (including the line itself), we use "≥" or ">".
Step 4: Write the inequality:
Using the inequality symbol determined in step 3 and the equation of the line, write the inequality. In our example, if the shading is above the line (including the line itself), we would write the inequality as y ≥ 2x + 3.
Remember to adjust the variables or coefficients based on the specific equation of the line in your graph.
To write an inequality for a graph, we need to analyze the characteristics of the graph and then determine the appropriate inequality statement to represent those characteristics. The steps to do this are as follows:
1. Understand the graph: Take a closer look at the given graph and determine its important features, such as intercepts, slopes, and regions above or below the line.
2. Identify the slope: If the graph is a straight line, determine its slope. To calculate the slope, choose two points on the line and use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
If the line is not straight, then it may not have a slope.
3. Determine the y-intercept: If the graph contains a point where the line crosses the y-axis (x = 0), then that point represents the y-intercept of the line.
4. Write the inequality: Based on the characteristics determined in steps 1-3, we can now write the appropriate inequality statement.
- If the line is solid (not dotted) and the region above the line is shaded, the inequality is of the form "y > mx + b" or "y ≥ mx + b" (greater than or equal to).
- If the line is solid (not dotted) and the region below the line is shaded, the inequality is of the form "y < mx + b" or "y ≤ mx + b" (less than or equal to).
- If the line is dotted, it means the points on the line are not included in the solution set, so we use either ">" or "<" instead of "≥" or "≤".
By following these steps and analyzing the given graph, you can write the appropriate inequality statement.