Section 3-6 Slope of Parallel and Perpendicular Lines SPI 22A: determine the equation of a line parallel or perpendicular to a given

Objectives:• Relate slope to parallel and perpendicular lines

Parallel lines: coplanar lines that do not intersect

Perpendicular lines: lines that intersect and form a right angle

Slopes of Parallel Lines (Definition)

If two non-vertical lines are parallel, then their slopes are equal.

If the slopes of two distinct non-vertical lines are equal, then the lines are parallel.

Any 2 vertical lines are parallel.

Checking for Parallel Lines

Slope of Line 1:

Slope of Line 2:

Slopes of Parallel Lines

Line a contains A(-4, 2) and B(3, 1).

Line b contains C(-4, 0) and D(8, -2).

Are lines a and b parallel? Explain.

The slope of a = -1/7 and the slope of b = -1/6.

Given two Equations, Determine if the lines are Parallel

What is the slope of 4y – 12x = 20?

Are the lines 4y – 12x = 20 and y = 3x – 1 parallel? Explain.

1. Change equation to slope-intercept form.

4y – 12x = 20 Given + 12x + 12x APE 4y = 12x + 20 DPE 4 4 4 y = 3x + 5

2. The slope is 3.

What is the slope of y = 3x – 1?

The slope is 3.

By Definition: The lines have the same slope.They are 2 distinct lines, since they have different y intercepts.Therefore, they are parallel.

Writing Equations of Parallel Lines

Write an equation for the line parallel to y = - 4x + 3 that contains (1, -2).

What is the slope of the equation y = - 4x + 3? - 4

What will be the slope of the equation containingcoordinate (1, -2)?

- 4

Which form of an equation will you use to write an equation given the slope and one point?

Point-slope form

Slopes of Perpendicular Lines (Definition)

If two non-vertical lines are perpendicular, then the product of their slopes is -1.

If the slopes of two lines have a product of -1, the lines are perpendicular.

Any horizontal line and vertical line are perpendicular.

Checking for Perpendicular Lines

1. If one line is vertical and the other horizontal, then they are perpendicular.

2. If the product of the slopes are -1, then they are .

Practice: Check for Perpendicular lines

13

7

9

4 ....... And

.3

7- is 4 of slope theand

9

4 is 3 of slope The

Writing Equations for Perpendicular lines

Write an equation for the line perpendicular toy = - 3x – 5, that contains (- 3, 7).

1. Write what you know, given the first equation.

y = - 3x – 5; Slope is -3.2. Find the slope of the line perpendicular to the given line. Think> What is the relationship between the 2 slopes?

The slope of the perpendicular line is the opposite reciprocal of the slope of the other line. Slope is 1/3.

3. Use point-slope form to write an equation.

Real-World Connection