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Understanding Slope Relationships in Lines | Study the Incline & Decline

Learn to find, classify, and understand slopes of lines given points, including parallel & perpendicular lines. Practice exercises and examples included.

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Understanding Slope Relationships in Lines | Study the Incline & Decline

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  1. Lesson 2.2: Find Slope Objectives: • To find the slope of a line given 2 points • To classify a line based on its slope • To find the slope of parallel and perpendicular lines

  2. Slope Anything that isn’t completely vertical has a slope. This is a value used to describe its incline or decline.

  3. Slope Definition The slopem of a nonvertical line is the ratio of vertical change (the rise) to the horizontal change (the run). ryse ryse

  4. Ex Find the slope of the line passing through the points (-4, 4) and (6, 2). Find the slope of the line passing through the points (3, -5) and (-3, 13).

  5. Your Turn! Find the slope of the line passing through the points: (3, 8) and (-6, -2) (-4, -4) and (-12, 2) (7, 13) and (7, 8) (-2, 5) and (-9, 5)

  6. Slope The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical.

  7. Ex Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. • (1, 6); (8, -1) • (-4, -3); (7, 1) • (-5, 3); (-5, 1) • (9, 2); (-9, 2)

  8. Parallel and Perpendicular Two lines are parallel lines iff they are coplanar and never intersect. Two lines are perpendicular lines iff they intersect to form a right angle.

  9. Parallel and Perpendicular Two lines are parallel lines iff they have the same slope. Two lines are perpendicular lines iff their slopes are negative reciprocals.

  10. Ex Tell whether the pair of lines are parallel, perpendicular, or neither. • Line 1: through (-2, 1) and (0, -5) Line 2: through (0, 10) and (-3, 1) • Line 1: through (-2, 2) and (0, -1) Line 2: through (-4, -1) and (2, 3)

  11. Ex Tell whether the pair of lines are parallel, perpendicular, or neither 3. Line 1: through (-2, 8) and (2, -4) Line 2: through (-5, 1) and (-2, 2) 4. Line 1: through (-4, -2) and (1, 7) Line 2: through (-1, -4) and (3, 5)

  12. Challenge Write an equation of any line that is parallel to the line y = 2x – 1 Write an equation of any line that is perpendicular to y = -3x + 4

  13. Homework Pg 86-87 #1 – 23

  14. 2.3 Graph Equations of Lines

  15. Parent Functions All other linear functions can be formed with transformations on the parent function. Linear parent function: y = x or f (x) = x.

  16. Examples Graph each equation. THEN compare to the parent graph. y = -2x y = 3x – 4 y = - x + 2 .

  17. Examples Graph each of the following: f (x) = 1 – 3x 6 – y = -2x 8y = -2x + 20 4x = -5y + 16

  18. Standard Form Standard Form of a Line The standard form of a linear equation is Ax + By = C, where A and B are not both zero. Ex:

  19. Standard Form To graph an equation in standard form: Write equation in standard form. Let x = 0 and solve for y. This is your y-intercept. Let y = 0 and solve for x. This is your x-intercept. Connect the dots. Ex:

  20. Examples Find the x and y intercepts. Then graph. 2x + 5y = 10 -2x – 3y = 6 8y = -2x + 20

  21. Horizontal and Vertical Lines Horizontal Line: Slope of 0 Looks like y = # Ex: y = 3 Vertical Line: Slope is undefined Looks like x = # Ex: x = 3

  22. Examples Graph each of the following: x = 1 y = -4 4x = -12 -4 – 2y = 6

  23. Examples Graph each equation using any method. 8y = 4x - 16 y – 7 = -2x x + y = -3

  24. Assignment Pg 93 #11 – 17, 21 – 23, 24 – 29 (AND GRAPH), 33, 34, 43 – 49, 52, 53

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