Lesson 2 2 Find Slope Objectives 1 To

Lesson 2. 2: Find Slope Objectives: 1. To find the slope of a line given 2 points 2. To classify a line based on its slope 3. To find the slope of parallel and perpendicular lines

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

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

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).

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)

Slope The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical. m>0 m<0 m=0 m = undef Insert Picture

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

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.

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.

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

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)

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

Homework Pg 86 -87 #1 – 23

2. 3 Graph Equations of Lines

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

Examples Graph each equation. THEN compare to the parent graph. 1. y = -2 x 2. y = 3 x – 4 3. y = - x + 2 4. .

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

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:

Standard Form Ex: To graph an equation in standard form: 1. Write equation in standard form. 2. Let x = 0 and solve for y. This is your yintercept. 3. Let y = 0 and solve for x. This is your xintercept. 4. Connect the dots.