3 4 Find and Use Slopes of Lines

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 • 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? 1. Line 1: (-3, 1), (-7, -2) Line 2: (2, -1), (8, 4) 2. Line 1: (-2, -1), (1, -2) Line 2: (-5, -3), (-1, -4) 3. Line 1: (-3, -2), (1, 2) Line 2: (1, 3), (4, 6)

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). 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? 1. Line 1: (1, 1), (3, 3) Line 2: (2, 2), (0, 4) 2. 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 •