The Slope of a Line Finding Slope of

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The Slope of a Line

The Slope of a Line

Finding Slope of a Line • The method for finding the steepness of stairs

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.

Finding the Slope of a Line • The steepness of the line is the

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.

Important things about slope… • Slope is the change in y over change in

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)

Formula for slope:

Formula for slope:

Find the slope of a line passing through points (-2, 4) and (3, 6)

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

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

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

A slope of -3/2 means that or every time y goes down 3, x

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

Classify lines by their slope: y x 1. A line with a positive slope

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

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

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

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

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

4. A line with an undefined slope is vertical (m is undefined) YOU CANT

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

Find the slope by using the graph. 4 3 2 1 -4 -3 -2

Find the slope by using the graph. 4 3 2 1 -4 -3 -2 -1 -1 1 -2 -3 -4 2 3 4 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.

Find the slope by using the graph. 4 3 2 1 -4 -3 -2

Find the slope by using the graph. 4 3 2 1 -4 -3 -2 -1 -1 1 -2 -3 -4 2 3 4 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.