4.4 Slope of a Line

Slope – a measure of how steep a line is.

Slope is the ratio of the vertical change to the horizontal change of a non-vertical line.

Section 4.4 Slope of a Line

Rise = “The change in Y” Run “The change in x”

RISE

RUNRise = 5Run 7

Formula: Slope = rise = y2 - y1

run x2 - x1

= “The change in Y” “The change in x”

(X2, Y2)

(X1, Y1)

Positive Slope

Negative Slope

Horizontal Line= Zero Slope

Vertical Line= No Slope orUndefined Slope

Examples Find the slope of the order pairs.

1. (4,4),(9,10) Slope = 10-4 = 6 9-4 5 2. (3,2),(2,3) 3. (-1,4),(3,-2)

Answers 2. (3,2),(2,3) 3-2 = 1 = -1 2-3 -1 3. (-1,4),(3,-2) -2-(4) = -6 = -3 3-(-1) 4 2

Parallel Lines – have the same slope

These lines are parallel -- The rise/run ratio of both lines is the same

Perpendicular Lines – the lines have slopes that are negative reciprocals of each other

If this line has a slope of –2/3 …..

Then the slope of any perpendicular line must be 3/2

Tell whether the lines are parallel, perpendicular, or neither.

Line 1: through (3,2) and (5,7)

Line 2: through (0,3) and (-5,5)

Find the slope of each line, then compare….

Line 1: slope = 7-2 = 5

5-3 2

Line 2: slope = 5-3 = 2

-5-0 -5

-2/5 is the negative reciprocal of 5/2, so these lines are perpendicular.

Line 1: Through (-3,1) and (3,4)

Line 2: Through (-4,-3) and (4,1)

Each line has a slope of ½ , so the lines are parallel.

Tell whether the lines are parallel, perpendicular, or neither.

Homework

Text page 230, #20-50 even AND # 51