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The Slope of a Line

The Slope of a Line. Focus 7 - Learning Goal #1: The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. Finding Slope of a Line.

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The Slope of a Line

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  1. The Slope of a Line

  2. Focus 7 - Learning Goal #1:The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities.

  3. Finding Slope of a Line • The method for finding the steepness of stairs suggests a way to find the steepness of a line. • A line drawn from the bottom step to the top set of a set of stairs touches each step in one point. • The rise and the run of a step are the vertical and the horizontal changes, respectively, between two points on the line.

  4. Finding the Slope of a Line • The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step. • We call the steepness of a line its slope.

  5. Important things about slope… • Slope is the change in y over change in x. • Slope is represented by the letter m • Vertical line has NO slope (undefined) • Horizontal line has a slope zero (0)

  6. Formula for slope:

  7. Find the slope of a line passing through points (-2,4) and (3,6) 6 - 4 2 m = = 3 - -2 5

  8. Find the slope of a line passing through points (1,1) and (3,-2) -2 - 1 3 m = = - 3 - 1 2

  9. A slope of -3/2 means that or every time y goes down 3, x moves over 2 Graph and count to check.

  10. Classify lines by their slope: y x 1. A line with a positive slope rises from left to right (m>0)

  11. 2. A line with a negative slope falls down from left to right (m<0) y x

  12. 3. A line with a zero slope is horizontal (m=0) Equation y = 3 y x

  13. 4. A line with an undefined slope is vertical (m is undefined) YOU CANT DIVIDE BY 0! y x

  14. Find the slope by using the graph. To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary. This line goes up 2 and over 1. The slope is 2/1 or 2.

  15. Find the slope by using the graph. To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary. This line goes down 2 and over 1. The slope is -2/1 or -2.

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