Math Problem Statement

Determine the slope of the line.

Solution

To determine the slope of the line in the graph:

  1. Identify two points on the line: From the image, two clear points are (4,4)(-4, 4) and (4,4)(4, -4).

  2. Use the slope formula:
    m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}
    Substituting the coordinates (x1,y1)=(4,4)(x_1, y_1) = (-4, 4) and (x2,y2)=(4,4)(x_2, y_2) = (4, -4):
    m=444(4)=84+4=88=1m = \frac{-4 - 4}{4 - (-4)} = \frac{-8}{4 + 4} = \frac{-8}{8} = -1

  3. Conclusion: The slope of the line is m=1m = -1.

Would you like a further breakdown or additional examples?


Here are five related questions to deepen understanding:

  1. What is the slope of a vertical line?
  2. How does the slope of a horizontal line compare to that of a diagonal line?
  3. If the slope of a line is 00, what does the graph look like?
  4. How does changing the sign of the slope affect the direction of the line?
  5. What does a slope of 11 represent on a graph?

Tip: Always simplify your slope fraction to its lowest terms to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Geometry
Slope of a Line
Linear Equations

Formulas

m = (y2 - y1) / (x2 - x1)

Theorems

Slope formula

Suitable Grade Level

Grades 6-8