University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

56

Pages:

1
Author:

Michael Haley

Mini-Lecture 3.4 Slope and Rate of Change Learning Objectives: 1. 2. 3. 4. 5. Find the slope of a line given two points of the line. Find the slope of a line given its equation. Find the slopes of horizontal and vertical lines. Compare the slopes of parallel and perpendicular lines. Slope as a rate of change. Examples: 1. Find the slope of the line that passes through the given points. a) (6, 5) and (1, 7) b) c) (-5, 0) and (0, -3) a) x + y = 12 b) 3 x + y = 8 c) 11x − 3 y = 33 d) 9 x + y = −12 e) 2. Find the slope of each line. y+5=0 f) 2 x − 7 = 0 3. Determine whether each pair of lines is parallel, perpendicular, or neither. a) 3x = 2 y + 3 2x + 3y = 2 b) x + 3y = 4 8x + 2 y = 2 c) 9 x = 16 − 3 y 16 − 4 y = 12 x Find the slope of a line that is (a) parallel and (b) perpendicular to the line passing through each pair of points. d) (−5, −5) and (−1, −1) e) (−2,10) and (5, −4) 4. An inclined ramp leading to a warehouse is to rise 16 inches for each horizontal distance of 17 feet. Write this slope as a grade. (Round to the nearest tenth of a percent, if necessary). Teaching Notes: • • • Many students confuse the change in y and change in x in the slope formula. Hint: if you ____ can imagine a picnic table (X X), the x is on the bottom. If the y is on the bottom (Y Y ), the picnic table will fall over! Remind students to “read” the slope of the line as it moves from left to right. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) − 2 5 3 11 ; 1b) ; 1c) − ; 2a) -1, 2b) -3; 2c) ; 2d) -9; 2e) 0; 2f) undefined; 5 4 5 3 3a) perpendicular; 3b) neither; 3c) parallel; 3d) a: 1, b: –1; 3e) a: -2, b: 1/2 ; 4) 4/51 or 7.8%