Slopes and Parallel Lines

Goals:To find slopes of linesTo identify parallel linesTo write equations of parallel lines

Slope

1y

2x1x

riseslope

run

2y

2 1

2 1

y

x

ym

x

..

2 1 ( )x runx

2 1 ( )y risey

Example Find the slope of A (2,3) and B (6,4).

1

4

4 36 2

m

1,x 2 ,x 2y1y

Comparing Slopes of Lines Two non-vertical lines are parallel if and only if they have

the same slope. Vertical lines are parallel. Are these lines parallel?

(6,4)

l pmm

..

.

.

(5, 1)

( 4,0)

( 1, 3)

l

p

4 0 4 2

6 ( 4) 10 5lm

1 ( 3) 2 1

5 ( 1) 6 3pm

Equation of a line in slope-intercept form

Slope-intercept form:

y mx b

int

m slope

b y ercept

Positive slope (the line rises from left to right)

Negative slope (the line falls from left to right)

Examples Write an equation of a line passing through (2,3) having a

slope of 5.

2,3

y mx b , yx

3 5(2) b

7b

5 7y x

5 7y x

.

Equation of a horizontal and vertical line

The slope of a horizontal line is zero. Why?

The slope of a vertical line is undefined. Why?

4x

3y .

.

.

. 0m

Writing EquationsWrite an equation passing through (-4,3) and parallel to 1. Find the slope of a line that is parallel to this line.2. Use this slope and the point given to find b.3. Write the equation.

What do the graphs of these equations look like?

2 5y x

2m

3 2( 4)

3 8

5

y mx b

b

b

b

2 5y x

2 5y x

StudentsAre lines l and p parallel?

(7,5)

.

.

.

.

(6, 1)

( 5,0)

( 6, 6)

l

p

Students 1. What is the equation of a line that passes through C(9,-

2) that has a slope of 1/3?

2. Write an equation passing through (2,3) and parallel to

31

2y x