Math Problem Statement

Determine the slope of the given line from the graph.

Solution

The graph in the image shows a straight line with a positive slope. The slope (mm) of a line is calculated using the formula:

m=ΔyΔx=RiseRunm = \frac{\Delta y}{\Delta x} = \frac{\text{Rise}}{\text{Run}}

To determine the slope:

  1. Select two clear points on the line where it crosses the grid intersections. For example:

    • Point 1: (10,0)(-10, 0)
    • Point 2: (10,6)(10, 6)
  2. Compute the changes in yy and xx:

    • Δy=y2y1=60=6\Delta y = y_2 - y_1 = 6 - 0 = 6
    • Δx=x2x1=10(10)=10+10=20\Delta x = x_2 - x_1 = 10 - (-10) = 10 + 10 = 20
  3. Substitute into the slope formula: m=ΔyΔx=620=310m = \frac{\Delta y}{\Delta x} = \frac{6}{20} = \frac{3}{10}

Thus, the slope of the line is:

310\boxed{\frac{3}{10}}

Would you like further details or clarification on this? Here are some related questions to explore further:

  1. What does the slope of a line represent geometrically and practically?
  2. How does the slope affect the steepness of a line?
  3. How can you identify if a line has a positive or negative slope from a graph?
  4. What are the slope-intercept and point-slope forms of the equation of a line?
  5. How can slope calculations be extended to real-world applications?

Tip: Always double-check that your selected points align exactly with grid intersections to avoid errors when calculating the slope.

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Math Problem Analysis

Mathematical Concepts

Slope of a Line
Linear Algebra
Coordinate Geometry

Formulas

m = Δy / Δx

Theorems

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Suitable Grade Level

Grades 7-8