parallel & perpendicular lines slope of parallel lines two non-vertical lines with the same...

Parallel & Perpendicular Lines

Slope of Parallel Lines

• Two non-vertical lines with the same slope are parallel.

Parallel Lines

43 xy23 xy

The equations of two parallel lines have the same slope, but two different y-intercepts.

Parallel lines have the same slope

If Line A has a slope of 4 (m = 4),

then which of these four lines is parallel to Line A?

Line B, m = 16

Line C, m = 12

Line D, m = 4

Line E, m = 2/3

y = 3x + 4 and y = 3x - 2

y = 3x + 4

y = 3x -2

BACK

Are the two lines: L1, through (-2, 1) and (4, 5)L2, through (3, 0) and (0, -2),

parallel?

)0()3(

)2()0(2

m

)2()4(

)1()5(1

m

6

4

3

2

3

2

Slopes of Perpendicular Lines

• If neither line is vertical, then the slopes of perpendicular lines are negative reciprocals.

• If the product of the slopes of two lines is -1 then the lines are perpendicular.

• Horizontal lines are perpendicular to vertical lines.

x-axis

y-axis

Perpendicular Slopes4

31

m

3

42 m 4

3

What can we say about the intersection of the two lines?

Write parallel perpendicular or neither for the pair of lines that passes through (5, -9) and (3, 7) and the line through (0, 2) and (8, 3).

)5()3(

)9()7(1

m

)0()8(

)2()3(2

m

2

16

8

8

1

1

8

8

18

8 1

Perpendicular lines have the ‘opposite reciprocal’ slope

To get the opposite reciprocal…

Express the slope as a fraction

Then flip it and give it the opposite sign!

Perpendicular lines have the ‘opposite reciprocal’ slope

So, a line with slope 3 is perpendicular to a line with slope –1/3

Perpendicular lines have the ‘opposite reciprocal’ slope

If Line A has a slope of –4/5 (m = -4/5), then which of these four lines is perpendicular to Line A?

Line B, m = 9

Line C, m = 5/4

Line D, m = 20

Line E, m = -5/4

bmxy Slope-Intercept Form

•Useful for graphing since m is the slope and b is the y-intercept

11 xxmyy Point-Slope Form

•Use this form when you know a point on the line and the slope

•Also can use this version if you have two points on the line because you can first find the slope using the slope formula and then use one of the points and the slope in this equation.

0 cbyax Standard Form

•Commonly used to write linear equation problems or express answers

Remember parallel lines have the same slopes so if you need the slope of a line parallel to a given line, simply find the slope of the given line and the slope you want for a parallel line will be the same.

Perpendicular lines have negative reciprocal slopes so if you need the slope of a line perpendicular to a given line, simply find the slope of the given line, take its reciprocal (flip it over) and make it negative.

3

1m

3

1m

3

1m

31

3m

Rules and PropertiesParallel Lines

Parallel lines have the same slope.

Parallel & Perpendicular Lines

Algebra 1

&

Algebra 1 Honors