5.6 Parallel and Perpendicular Lines

What you’ll learn:1. To write an equation of the line

that passes through a given point, parallel to a given line.

2. To write an equation of the line that passes through a given point,

perpendicular to a given line.

Parallel Lines

Parallel lines – lines in the same plane that do not intersect.

Parallel lines have the same slope.All vertical lines (with an undefined slope) are

parallel.If the graph of the equation y=4x-5 is parallel to

another line, they both have a slope of 4.

Perpendicular Lines

Perpendicular lines – lines that intersect at right angles.

Two nonvertical lines are perpendicular if their slopes are negative reciprocals of each other. (Change sign and flip over)

ex: m=-3, perpendicular slope: ⅓m=-⅙, perpendicular slope: 6

Writing equations when lines are parallel.

If you are given an equation and are asked to create an equation for a line that is parallel to that line, use the following steps:

1. Find the slope of the equation. (Solve for y, slope is the number in front of x)

2. Use that slope and the point that is given to find b. (plug into y=mx+b)

3. Take the m and b that you found and plug them into y=mx+b

Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of

each equation.

1. y=-3x+7, (-2,5)find m (already solved for y)

m=-3.Find b (plug into y=mx+b)

5=-3(-2)+b5=6+b-1=b

Plug m and b into y=mx+by=-3x-1

2. -2x+y=5, (0,-4)Solve for y in order to find m

y=2x+5m=2

Find b-4=2(0)+b-4=b

Plug m and b into y=mx+by=2x-4

Writing equations when lines are perpendicular

If you are given an equation and are asked to create an equation for a line that is perpendicular to that line, use the following steps:

1. Find the slope of the equation. (Solve for y, slope is the number in front of x)

2. Take that slope and flip it and change the sign to find the slope of the line that is perpendicular. Use that and the point that is given to find b. (plug into y=mx+b)

3. Take the m and b that you found and plug them into y=mx+b

Write the slope intercept form of an equation that passes through the given point and is perpendicular to the graph

of each equation.

1. y=-4x+3, (1,-3)m=-4, perpendicular slope: ¼Find b. -3=¼(1)+b-3=¼+b-3¼=bPlug m and b into y=mx+by=¼x-3¼

2. ⅓x+y=-7, (-2,-4)Solve for y to find m

y=-⅓x-7m=-⅓, perpendicular slope=3Find b-4=3(-2)+b-4=-6+b2=bPlug into y=mx+by=3x+2

Classworkp. 296

14-36 even, 50-52 all