Section 7.3Slope of a Line

Slope is a number that measures the steepness of a line.

The symbol for slope is m

Slope = m = Vertical Change = Rise Horizontal Change Run

Slope = m = y2 – y1

x2 – x1

SLOPE

Slope can be positive or negative.

The closer slope is to 0, the flatter the line.

The further slope is from 0, the steeper the line.

Characteristics of slope

If you’re given the graph, you can just count using Rise .

Run1. Find 2 points on the line (go left to right)2. Count how many UP or DOWN. That’s the

RISE.3. Count how many to the RIGHT. That’s the

RUN.4. Set up the fraction and reduce if possible.

To find slope…

Examples… see graph paper

If you’re given 2 ordered pairs, use the formula m = y2 – y1

x2 – x1

Label one point (x1, y1) and label the 2nd point (x2, y2).

Sub the x- and y-values into the formula. Simplify

To find slope…

1. (2, 4) and (-1, 3) 2. (8, 0) and (4, -2) 3. (-2, 3) and (-2, -5) 4. (-1, 8) and (1/3, -1)

EX: Find the slope of the line through the given points:

Plot the given point, then use Rise Run

1. Go up or down for the “Rise.”2. Go to the right for the “Run.”3. Plot a 2nd point.4. REPEAT steps 1 – 3 to get a 3rd point.5. Connect all 3 points with a straight line.

Graphing with Slope

1. Through (-1, -2) with m = -2 2. Through (-3, 4) with m = -2/3 3. Through (-2, 5) with m = 1 4. Through (-1, 5) with m = 4/5

Ex: Graph the line with the given slope that goes through the given point.

If the line is Horizontal… It’s all Run & no Rise. m = Rise = 0 m = 0

Run any #

If the line is Vertical… It’s all Rise and no Run.

m = Rise = any # m = undefined

Run 0

Horizontal and Vertical Lines

…(1, 4) with m = 0

…(-2, 3) with slope undefined

Graph the line through the point…

Parallel Lines are 2 lines that lie in the same plane but do not intersect. They have equal slopes. ◦ The symbol for parallel is ||

Perpendicular Lines are 2 lines that intersect at a 90o angle. Their slopes are opposite reciprocals.◦ The symbol for perpendicular is |

Parallel and Perpendicular Lines

1. m1 = -1 m2 = -1 2. m1 = -1/3 m2 = -3 3. m1 = ¼ m2 = -4 4. m1 = 0 m2 is undefined

Ex: Do the 2 slopes represent || lines, | lines, or neither?