Section 3 4 Slope of a Line Slope

Section 3. 4 Slope of a Line

Slope of a Line – the steepness or tilt of a line. When finding slope, it makes no difference which point is identified as (x 1, y 1) and which is identified as (x 2, y 2). Just remember that whatever y-value is first in the numerator, its corresponding x-value is first in the denominator.

Examples: Find the slope of the line that passes through the given points. 1) (-2, 8), (4, 3) 2) (-3, -4), (-1, 6)

Appearance of Lines with Given Slopes y Positive Slope Line goes up to the right m>0 Negative Slope Line goes downward to the right m<0 x y x Lines with positive slopes go upward as x increases. Lines with negative slopes go downward as x increases.

Appearance of Lines with Given Slopes y Zero Slope horizontal line y=b Undefined Slope vertical line x=a x y x

Slope-Intercept Form When a linear equation in two variables in written in slope-intercept form, slope y-intercept is (0, b) y = mx + b the m is the slope of the line and (0, b) is the y-intercept of the line.

Examples: Find the slope and y-intercept of the given line. 3) 2 x – 4 y = 8 4) -3 x – 4 y = 6

Parallel and Perpendicular Lines Two nonvertical lines are parallel if they have the same slope and different yintercepts. y Two nonvertical lines are perpendicular if their slopes are opposite reciprocals. y x x

Examples: Are the following lines parallel, perpendicular, or neither. 10) – 5 x + y = – 6 x + 5 y = 5 11) -8 x + 20 y = 7 2 x – 5 y = 0