Algebra 2

Chapter 2.4bWriting Linear Equations

Target Goals:1. Write an equation of a line parallel or

perpendicular to a given line

Parallel Lines

• Characteristics of PARALLEL lines:– Never cross– Run next to each other forever without crossing– Same steepness– SAME SLOPE!!!

Parallel Lines

Perpendicular Lines

• Characteristics of Perpendicular lines:– Cross– Cross at right angles (90°)– OPPOSITE RECIPROCAL SLOPES!!!

Perpendicular Lines

Parallel vs. Perpendicular • PARALLEL LINES have EQUAL slopes while

PERPENDICULAR LINES have OPPOSITE RECIPROCAL slopes.

• PARALLEL = EQUAL SLOPES• PERPENDICULAR OPPOSITE RECIPROCAL

SLOPES

Ex 1) Write an equation in slope-intercept form of a line that passes through (3, 7) and is parallel to the line with equation 3

54

y x

y mx b

Slope of the given line?

3/4

Slope-intercept form?

37 3

4b

97

4b

974b

28 9

4 4b

19

4b

3 19

4 4y x

37 3

4y x

3 97

4 4y x

3 97

4 4y x

3 9 28

4 4 4y x

3 19

4 4y x

Ex 2) Write an equation in slope-intercept form for the line that passes through (3, -2) that is perpendicular to the line with equation y = -5x + 1

y mx b

Slope of the given line?

-5

Slope-intercept form?

Slope of a perpendicular line?

1/5

12 35

b

325b

325b

10 3

5 5b

13

5b

1 13

5 5y x

12 35

y x

1 325 5

y x 1 3

25 5

y x

1 3 10

5 5 5y x

1 13

5 5y x