5.3 Slopes of Straight Lines

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5.3 Slopes of Straight Lines Hubarth Math 90

Ex 3 Finding the Slope Using a Graph Finding Slope Ex 3 Finding the Slope Using a Graph Find the slope of each line. a. slope = rise run 4 – 1 0 – 2 = The slope of the line is – . 3 2 = 3 –2 = – 3 2 b. slope = rise run The slope of the line is 2. –1 – 1 –2 – (–1) = = –2 –1 = 2

Ex 1 Finding Slope Using Points Find the slope of the line through E(3, –2) and F(–2, –1). slope = y2 – y1 x2 – x1 Substitute (–2, –1) for (x2, y2) and (3, –2) for (x1, y1). –1 – (–2) –2 – 3 = = – 1 5 = –5 Simplify. The slope of EF is – . 1 5

Ex 2 Horizontal and Vertical Lines Find the slope of each line. a. slope = y2 – y1 x2 – x1 2 – 2 1 – (–4) = Substitute (1, 2) for (x2, y2) and (–4, 2) for (x1, y1). = 5 Simplify. The slope of the horizontal line is 0. = 0 slope = y2 – y1 x2 – x1 b. Substitute (2, 1) for (x2, y2) and (2, –4) for (x1, y1). = 1 – (–4) 2 – 2 = 5 Simplify. Division by zero is undefined. The slope of the vertical line is undefined.

Summary Slope of Lines A line with a Positive slope slants upward from left to right A line with a negative slope slants downward from left to right A line with a slope of 0 is horizontal A line with an undefined slope is vertical. if the denominator is 0, then the slope is undefined

Ex 3 Identifying Slope and Y-intercept What are the slope and y-intercept of y = 2x – 3 then graph? mx + b y = 2x – 3 Use the Slope-Intercept form. slope, m = 2 y-intercept, b = (0, -3)

Ex 4 Writing an Equations 2 5 Write an equation of the line with slope and y-intercept 4 then graph. Use the slope-intercept form. y = mx + b y = x + 4 2 5 Substitute for m and 4 for b.

. . Practice 1. Find the slope of a line passing through the points a. (3, 4) and (-2, 3) b. (-2, 5) and (-3, 6) 𝑚= 1 5 𝑚= 1 −1 =−1 2. Find the slope from the given graphs. a. . b. c. . (2, 2) (-1, 0) 𝑚= 2 3 m=0 undefined 3. Find the slope and y-intercept of each equation and then graph.