Summary: Identifying and Using Slope

Key Concepts

Find the slope from a graph

  1. Locate two points on the line whose coordinates are integers.
  2. Starting with the point on the left, sketch a right triangle, going from the first point to the second point.
  3. Count the rise and the run on the legs of the triangle.
  4. Take the ratio of rise to run to find the slope, [latex]m={\Large\frac{\text{rise}}{\text{run}}}[/latex]
  • Slope of a Horizontal Line
    • The slope of a horizontal line, [latex]y=b[/latex] , is [latex]0[/latex].
  • Slope of a Vertical Line
    • The slope of a vertical line, [latex]x=a[/latex] , is undefined.
  • Slope Formula
    • The slope of the line between two points [latex]\left({x}_{1},{y}_{1}\right)[/latex] and [latex]\left({x}_{2},{y}_{2}\right)[/latex] is [latex]m={\Large\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}}[/latex]
  • Graph a line given a point and a slope.
    1. Plot the given point.
    2. Use the slope formula to identify the rise and the run.
    3. Starting at the given point, count out the rise and run to mark the second point.
    4. Connect the points with a line.



slope of a line
The slope of a line is [latex]m={\Large\frac{\text{rise}}{\text{run}}}[/latex] . The rise measures the vertical change and the run measures the horizontal change.