Which of the following graphs show the solution set to the inequality above?

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Understand the Problem

The question is asking which of the provided graphs represents the solution set to the inequality y < 3x + 4. We need to identify between options A, B, C, and D, which graph shows the correct region shaded below the line 3x + 4, along with understanding whether the line is included or not (dashed since it is <).

Answer

The solution set for the inequality $y < 3x + 4$ is represented by graph **A**.
Answer for screen readers

The correct answer is option A.

Steps to Solve

  1. Identify the equation of the line

The given inequality is $y < 3x + 4$. The equation of the line that forms the boundary is $y = 3x + 4$.

  1. Determine the type of line

Since the inequality is "<" (not "≤"), the line will be dashed. This indicates that points on the line itself are not included in the solution set.

  1. Find the y-intercept and slope

From the equation $y = 3x + 4$, the y-intercept is 4, and the slope is 3. This means the line crosses the y-axis at the point (0, 4) and rises 3 units for every 1 unit it moves to the right.

  1. Shade the correct region

Since we are looking for the region where $y$ is less than $3x + 4$, we will shade the area below the dashed line.

  1. Analyze the graph options

Review the provided graphs (A, B, C, and D) to see which one correctly represents a dashed line that crosses through (0, 4) and shades the area below the line.

The correct answer is option A.

More Information

In the inequality $y < 3x + 4$, the area below the dashed line represents all points where the y-value is less than the corresponding points on the line $3x + 4$. The dashed line indicates that points on the line are not included in the solution.

Tips

  • Confusing line types: Students might incorrectly use a solid line instead of a dashed line. Remember: "<" means the points on the line are not part of the solution.
  • Incorrectly choosing the shading area: Ensuring you shade below the line for the "less than" inequality is crucial.

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