Math Problem Statement

Select all of the true statements about the graph. Options include: whether the y-intercept of the red line is moved up or down, and comparisons of the slope between the red and black lines.

Solution

From the given graph and statements, let’s analyze each option:

  1. The y-intercept of the red line is moved down: The red line crosses the y-axis above zero, so it does not appear to have moved down.

  2. The slope of the red line is steeper: This is not true because the black line has a much steeper slope than the red line.

  3. The slope of the red line is less steep: This statement is true because the red line has a smaller slope (is less steep) than the black line.

  4. The y-intercept of the red line is moved up: The red line starts above the origin, so this could indicate a positive y-intercept.

  5. The slope of the red line is the same: This is not true because the red and black lines have different slopes.

  6. The y-intercept of the red line is the same: This is false, as the red and black lines have different y-intercepts.

Conclusion

The correct answer is:

  • The slope of the red line is less steep

Would you like more details or have any questions?

Related Questions

  1. How can we determine the slope of a line from a graph?
  2. How do we find the y-intercept of a line?
  3. What does it mean for a line to be "steeper" in mathematical terms?
  4. How does changing the slope affect a line's angle?
  5. How does the y-intercept affect where a line crosses the y-axis?

Tip

Remember, the slope indicates the "steepness" of a line, while the y-intercept shows where it crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graph Interpretation
Slope and Y-Intercept

Formulas

Slope = (change in y) / (change in x)

Theorems

Properties of Linear Functions

Suitable Grade Level

Grades 8-10