3.4 Find and Use Slopes of Lines

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3.4 Find and Use Slopes of Lines
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Basics of Slope

• Slope (of a Line) The vertical change (rise) of
  the line divided by the horizontal change (run)
  of the line.
• Slope is represented by the letter m in an
  equation.

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Types of slopes

• Negative Slope
• Driving Downhill
• m is negative
• Positive Slope
• Driving Uphill
• m is positive
• Zero Slope
• Driving on a flat road
• m is 0
• Undefined Slope
• A cliff or a wall
• m is undefined

Identify each type of slope in the graph above
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Find the Slope when given two points

• Remember slope is represented by m
• mrise/run
• 1. Label the x and y for each point
• 2. Rise
• The difference in vertical change
• Subtract the y-values as shown
• 3. Run-
• The difference in horizontal change
• Subtract the x-values as shown
• 4. Divide the rise by the run

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Find the slope of the line

• Remember slope is represented by m
• Label your x and y for each point
• Keep the slopes written as fractions
• 1. (0,4) and (4,0)
• 2. (0,4) and (5,8)
• 3. (-3, -2) and (4, 0)
• 4. (-2, 3) and (3, 3)
• 5. (2, -1) and (-1, 2)

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Comparing Slopes

• The steeper line has the slope with the greater
  absolute value.

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Parallel Slopes

• Two lines are parallel if they have the same slope

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Example Find the slope of each line. Which lines
are parallel?

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Your Turn

• Find the slope of each line. Are the two lines
  parallel?
• Line1 (-3, 1), (-7, -2)
• Line 2 (2, -1), (8, 4)
• 2. Line1 (-2, -1), (1, -2)
• Line 2 (-5, -3), (-1, -4)
• 3. Line 1 (-3, -2), (1, 2)
• Line 2 (1, 3), (4, 6)

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Perpendicular Slopes

• Two lines are perpendicular if the product of
  their slopes is equal to -1.
• The two slopes will be negative reciprocals
• Negative reciprocal Flip the fraction and change
  the sign

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Example Line h passes through (3, 0) and (7, 6).
Graph the line perpendicular to h that passes
through the point (2, 5).

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Your Turn

• Find the slope of each line. Are the two lines
  perpendicular?
• Line 1 (1, 1), (3, 3)
• Line 2 (2, 2), (0,4)
• Line 1 (-5, 2), (-3, 5)
• Line 2 (-2, 2), (1, 0)
• 3. Line 1 (-2, 3), (-5, 2)
• Line 2 (4, 1), (5, 3)

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Graph a line given the slope and a point

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