Lines. Slope Measure of units the line rises for each unit of horizontal change - symbol (m) m = Δy = y 2 – y 1 Δx x 2 – x 1 if x 2 = x 1 then m is undefined.

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Presentation transcript:

Lines

Slope Measure of units the line rises for each unit of horizontal change - symbol (m) m = Δy = y 2 – y 1 Δx x 2 – x 1 if x 2 = x 1 then m is undefined (vertical line)

Equation of Line Point-slope form y – y 1 = m (x – x 1 ) Example: Find the equation of a line that has a slope of 3 and passes through the point (1, -2)

Find the equation of the line that passes through the points (-3, 6) and (1, 2)

Slope-Intercept Form y = mx + b (0, b) is the y-intercept Sketch the following: a) y = 2x + 1 b) y = 2 c) 3y + x – 6 = 0

General Form Ax + By + C = 0

Rate of Change Slope can be considered a ratio or rate of change (average rate of change) Example: The population in a city was 3,687,000 in 1990 and 4,042,000 in What is the average rate of change over this time period? What does it tell you?

Two lines are parallel if m 1 = m 2 Find the equation for a line that passes through the point (2, -1) and is parallel to the line 2x – 3y = 5.

Two lines are perpendicular if m 1 = -1/m 2 Find the equation of a line that passes through the point (2, -1) and is perpendicular to the line 2x – 3y = 5

Homework Pg. 16 # 1, 3, 5, 9, 11, 13, 19, 22, 23-27, 31, 33, 36, 39, 45, 47, 59, 62