Math Problem Statement

Find the slope of the line in the provided graph.

Solution

To find the slope of the line in the graph, let's follow these steps:

  1. Identify Two Points on the Line: From the graph, we can observe that two points on the line are:

    • Point 1: (4,4)(-4, 4)
    • Point 2: (4,4)(4, -4)
  2. Use the Slope Formula: The formula for the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

  3. Substitute the Points: m=444(4)m = \frac{-4 - 4}{4 - (-4)} m=88=1m = \frac{-8}{8} = -1

Therefore, the slope of the line is -1.

Would you like more details on slope calculation or any additional assistance?

Here are five questions to further explore this topic:

  1. How do you interpret a negative slope on a graph?
  2. What are the characteristics of a line with a slope of -1?
  3. How does changing the points used affect the slope calculation?
  4. What does it mean if a line has a slope of 0?
  5. How would you find the equation of this line?

Tip: When finding the slope, choose points that are easy to read on the grid to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10