MATH 017 Intermediate Algebra S. Rook Slope of a Line MATH 017 Intermediate Algebra S. Rook

Overview Section 3.4 in the textbook Definition and properties of slope Slope-intercept form of a line Slopes of horizontal and vertical lines Slopes of parallel and perpendicular lines

Definition and Properties of Slope

Definition and Properties of Slope Slope (m): the ratio of the change in y (Δ y) and the change in x (Δ x) Quantifies (puts a numerical value on) the “steepness” of a line Given 2 points on a line, we can find its slope:

Definition and Properties of Slope (Example) Ex 1: Find the slope of the line containing (7, -1) and (4, 3)

Definition and Properties of Slope (Example) Ex 2: Find the slope of the line containing (-6, -8) and (-8, -12)

Sign of the Slope of a Line To determine the sign of the slope, examine the line from left to right Positive if the line rises Negative if the line drops

Slope-Intercept Form

Slope-Intercept Form Slope-intercept form: a linear equation in the form y = mx + b where m is the slope b is the y-coordinate of the y-intercept (0, b) Remember, to utilize the slope-intercept form of a line, y must be ISOLATED

Slope-Intercept Form (Example) Ex 3: Find the slope and y-intercept of y = 7x + 3

Slope-Intercept Form (Example) Ex 4: Find the slope and y-intercept of 4x – 5y = 25

Slope-Intercept Form (Example) Ex 5: Find the slope and y-intercept of 2x + 8y = 10

Slopes of Horizontal and Vertical Lines

Slopes of Horizontal and Vertical Lines Suppose we have a horizontal line y = 2 2 points on this line would be (a, 2) and (b, 2) Applying the slope formula, we have a slope of 0 Thus, we can say ALL horizontal lines have a slope of zero Suppose we have a vertical line x = -1 2 points on this line would be (-1, a) and (-1, b) Applying the slope formula, we have an undefined slope Thus, we can say ALL vertical lines have an undefined slope

Slopes of Horizontal and Vertical Lines (Example) Ex 6: Graph and give the slope of the line 4x = 4

Slopes of Horizontal and Vertical Lines (Example) Ex 7: Graph and give the slope of the line -6y = 10

Slopes of Parallel and Perpendicular Lines

Slopes of Parallel and Perpendicular Lines Parallel lines: two lines that have the SAME slope Perpendicular lines: two lines that have OPPOSITE RECIPROCAL slopes In other words, the product of the slopes is -1

Slopes of Parallel and Perpendicular Lines (Example) Ex 8: Determine whether 2x – y = 6 and 4x + 8y = 4 are parallel, perpendicular, or neither.

Slopes of Parallel and Perpendicular Lines (Example) Ex 9: Determine whether 3x + 5y = 2 and 8x + 2y = 6 are parallel, perpendicular, or neither.

Summary After studying these slides, you should know how to do the following: Understand the definition of slope and be able to apply the slope formula when given 2 points on a line Apply the definition of the slope-intercept form of a line to extract the slope and the y-intercept Be able to give the slope of a horizontal or vertical line Determine whether pairs of lines are parallel, perpendicular or neither