Math Problem Statement

Find the slope of the line graphed below.

Solution

To find the slope of the line shown in the graph, we can follow these steps:

  1. Identify Two Points on the Line: From the image, it appears there are two notable points on the line:

    • The first point is at (3,3)(-3, -3).
    • The second point is at (3,3)(3, 3).
  2. Use the Slope Formula: The formula for the slope (mm) of a line that passes through 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. Plug in the Points: Using (3,3)(-3, -3) as (x1,y1)(x_1, y_1) and (3,3)(3, 3) as (x2,y2)(x_2, y_2), m=3(3)3(3)=3+33+3=66=1m = \frac{3 - (-3)}{3 - (-3)} = \frac{3 + 3}{3 + 3} = \frac{6}{6} = 1

So, the slope of the line is 1.

If you have any questions or need further details, please let me know.

Here are some related questions for further practice:

  1. How do you find the slope of a line given its equation?
  2. What does a slope of zero indicate about a line?
  3. How do you interpret a negative slope on a graph?
  4. What is the slope-intercept form of a line?
  5. How would you find the slope if the points on the graph were decimals?

Tip: The slope indicates the steepness and direction of a line. A positive slope, like 1, means the line rises to the right.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Basic concept of slope in coordinate geometry

Suitable Grade Level

Grades 6-8