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Section 1-2 Slopes of Lines Slope The slope of a nonvertical line is a number measuring the steepness of the line relative to the x-axis; it is the ratio of the rise to the run. rise y 2 y1 m run x2 x1 Important facts about the slope of a line: 1. a. Horizontal lines have a slope of zero b. Vertical lines have no slope ** Having no slope is quite different from having zero slope – see diagram on p. 8 Important facts about the slope of a line: 2. Lines with positive slopes rise to the right – the greater the slope the more steeply the line rises – see diagram p. 8 Important facts about the slope of a line: 3. Lines with negative slopes fall to the right – the greater the absolute value of the slope the more steeply the line falls – see diagram p. 8 Slope of a line The slope of y = mx + k is m. Since m is a constant value, the slope of a line is constant. ** Since slope is constant, any two points on the line will give the same value for the slope. The numbers m and k in y = mx + k provide us with a mental picture of the line, m is the slope and k is the y-intercept. Slope-intercept form y = mx + k is the slope-intercept form. We are used to seeing y = mx + b – in this book they use k instead of b. Feel free to use b or k Slopes of Parallel Lines Two nonvertical lines are parallel if and only if they have the same slope. Activity page 10 a. 1 and 2 are complementary 1 and 3 are congruent b. 2 and 3 are complementary c. the red and blue segments are perpendicular rise a d. the slope of the red segment = run the slope of the blue segment b rise b b = run a a Slopes of Perpendicular Lines Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the slopes are and , then 1 m1 or m1 m2 1 m2 Example Find the slope of the line joining the given points: (2, -6) and (8, -3) Example Find the slope and y-intercept of the line whose equation is given: a. y = 3x + 4 b. 4x + 3y = 9 Example A line l has equation x + 2y = 5. What is the slope of a line parallel to line l? Perpendicular to line l? Example Find the value of k if the line joining (2, K) and (4, 5) are the line y = 3x + 1 are parallel? Perpendicular?