Math Problem Statement

Find the slope of the line shown in the graph by using the formula rise/run.

Solution

To find the slope of the line in the given graph, we follow the "rise over run" formula for the slope:

slope=riserun\text{slope} = \frac{\text{rise}}{\text{run}}

Step-by-Step Solution:

  1. Identify two points on the line: From the graph, two points are clearly marked:

    • Point 1: (2,1)(-2, 1)
    • Point 2: (2,1)(2, -1)
  2. Determine the rise and run:

    • Rise is the change in yy (the vertical change), which can be calculated as y2y1y_2 - y_1.
    • Run is the change in xx (the horizontal change), which is calculated as x2x1x_2 - x_1.
  3. Calculate the slope: Slope=y2y1x2x1=112(2)=24=12\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 1}{2 - (-2)} = \frac{-2}{4} = -\frac{1}{2}

Final Answer:

The slope of the line is 12-\frac{1}{2}.

Would you like more details or have any questions? Here are five related questions you might find useful:

  1. How do you determine the rise and run from two points on a graph?
  2. What is the relationship between a positive and negative slope?
  3. How does the slope formula change if the line is vertical or horizontal?
  4. Can you find the equation of the line given these points?
  5. What does the slope tell us about the direction of the line?

Tip: When choosing points from a graph, make sure they are clear intersections on the grid lines to avoid errors in calculation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope Calculation

Formulas

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

Theorems

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Suitable Grade Level

Grade 7