Section 13.2 State and apply the slope formula. Slope (Steepness) The ratio of the change in y (vertical change or rise) to the change in x (horizontal.

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Presentation transcript:

Section 13.2 State and apply the slope formula

Slope (Steepness) The ratio of the change in y (vertical change or rise) to the change in x (horizontal change or run). Denoted by m. Slope m = = The slope of a line does not depend on the order in which points are chosen because O x y (x₁, y₁ ) (x ₂, y ₂ ) x₂- x ₁ y₂- y ₁

Slope Facts: 1. The greater the slope’s absolute value, the steeper the line. 2. Lines with positive slopes rise to the right. 3. Lines with negative slope fall to the right. O O y y x x

Slope Facts: 4. The slope of a horizontal line is zero. y ₁ = y ₂ 5.The slope of a vertical line in not defined. x ₁ = x ₂ O O y y x x Slope = 0 No Slope

Example 1: Complete with always, sometimes, or never. a.The slope of a vertical line is _______________ zero. b.The slope of a horizontal line is _______________ zero. c.The slope of a line that rises to the right is ________________ positive. d.The slope of a line that falls to the right is ________________ negative. Example 2: Find the slope of the line through the two points named. If the slope is not defined, write not defined. a.(-3, 4), (-4, 5) b. (6, -3), (-1, -2) always never

Example 2 Continued: Find the slope of the line through the two points named. If the slope is not defined, write not defined. c.(8, -4), (-3, -4) d. (-6, -2), (-6, 9)

Practice 1: Name each line in the figure whose slope is positive, negative, zero, or not defined. a. b. c. d. Practice 2: Find the slope of the line through the points named. If the slope is not defined write not defined. a.(-4, 1); (3, 2)b. (6, -3); (2, -1)c. (-1, 4); (-1, -3) d. (-2, -1); (-4, -3)e. (-1, 7); (5, 7) O y x d c b a negative positive Not defined zero

Practice 3: Find the slope and length of if A = (-4, -3) and B = (0, 5). Practice 4: Show that R, S, and T are collinear by showing and have the same slope. R(4, -1), S(-5, 2), T(-2, 1). Slope = 2

Additional Practice: P531 Classroom exercises #1-6 Homework: P Written exercises #1, 2-20 even