Math Problem Statement

Find the slope of Lines A, B, and C using the graph provided.

Solution

From the graph provided, you are asked to find the slopes of three lines: Line A, Line B, and Line C.

To determine the slope of each line, use the formula for slope between two points: slope=ΔyΔx=y2y1x2x1\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

Analysis of the slopes:

  1. Line A (Blue): This line appears to be increasing from left to right, so the slope is positive.

    • It passes through points (0,0)(0, 0) and (2,1)(2, 1).
    • Slope = 1020=12=0.5\frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5.
  2. Line B (Red): This line is decreasing from left to right, so the slope is negative.

    • It passes through points (0,0)(0, 0) and (1,2)(1, -2).
    • Slope = 2010=2\frac{-2 - 0}{1 - 0} = -2.
  3. Line C (Green): This line is decreasing steeply from left to right, so the slope is negative.

    • It passes through points (0,0)(0, 0) and (1,1)(1, -1).
    • Slope = 1010=1\frac{-1 - 0}{1 - 0} = -1.

Final Slopes:

  • Slope of Line A: 0.50.5
  • Slope of Line B: 2-2
  • Slope of Line C: 1-1

Let me know if you need more details or explanations!

Related Questions:

  1. What is the significance of a positive versus negative slope?
  2. How do you determine if a line is steeper based on its slope?
  3. What happens to a line when the slope is zero?
  4. Can two different lines have the same slope but be distinct?
  5. How does the slope formula change if the line is vertical?

Tip: Always check if a line is horizontal or vertical because horizontal lines have a slope of 0, and vertical lines have an undefined slope.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 6-9