Section 7.3 Slope of a Line.

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Presentation transcript:

Section 7.3 Slope of a Line

SLOPE 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

Characteristics of 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.

To find slope… If you’re given the graph, you can just count using Rise . Run Find 2 points on the line (go left to right) Count how many UP or DOWN. That’s the RISE. Count how many to the RIGHT. That’s the RUN. Set up the fraction and reduce if possible.

Examples… see graph paper

To find slope… 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

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

Graphing with Slope Plot the given point, then use Rise Run Go up or down for the “Rise.” Go to the right for the “Run.” Plot a 2nd point. REPEAT steps 1 – 3 to get a 3rd point. Connect all 3 points with a straight line.

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

Horizontal and Vertical Lines 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

Graph the line through the point… …(1, 4) with m = 0 …(-2, 3) with slope undefined

Parallel and Perpendicular Lines 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 |

Ex: Do the 2 slopes represent || lines, | lines, or neither? 1. m1 = -1 m2 = -1 2. m1 = -1/3 m2 = -3 3. m1 = ¼ m2 = -4 4. m1 = 0 m2 is undefined