Math Problem Statement

Find the slope of the line graphed below.

Solution

From the image, the task is to find the slope of the given line. Let’s solve this step-by-step:

  1. Choose two points on the line: From the graph, two points on the line are:

    • (0,4)(0, 4)
    • (4,0)(4, 0)
  2. Use the slope formula: The slope mm is calculated as: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

    Substituting the points (x1,y1)=(0,4)(x_1, y_1) = (0, 4) and (x2,y2)=(4,0)(x_2, y_2) = (4, 0): m=0440=44=1m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1

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

Would you like more details or have any questions?

Related Practice Questions:

  1. What is the slope of a line passing through the points (2,3)(2, 3) and (5,7)(5, 7)?
  2. If the slope of a line is 2-2 and it passes through (0,1)(0, 1), what is the equation of the line?
  3. How do you determine if a line is horizontal or vertical based on its slope?
  4. If the slope of a line is 33, what is its rise and run?
  5. What does a slope of zero indicate about a line's orientation?

Tip: Always ensure to pick clear points on the graph when calculating the slope to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope Formula

Suitable Grade Level

Grades 6-8