3.4 Find and Use Slopes of Lines

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. Rise Run

Types of slopes Identify each type of slope in the graph above 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

Find the Slope when given two points Remember slope is represented by m m=rise/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 Rise Run

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) Rise Run

Comparing Slopes The steeper line has the slope with the greater absolute value.

Parallel Slopes Two lines are parallel if they have the same slope

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

Your Turn Find the slope of each line. Are the two lines parallel?

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

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

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)

Graph a line given the slope and a point