# Graphing Parallel and Perpendicular Lines

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Graphing Parallel and Perpendicular Lines

Review Slope Formula Slope intercept form y = mx + b b = y-intercept
m = slope

Parallel Lines If two nonvertical lines in the same plane have the same slope, they are parallel. Parallel lines Same slope Different y-intercepts

Examples of Parallel lines

Example Line 1: y = 2x + 1 Line 2: y = 2x - 3
These two lines are parallel because they have the same slope. No matter how far they continue on, they will NEVER cross each other!

Are these equations parallel?
1. 2. 3.

How do you write the equation for a parallel line with only a point and a slope?

Use these steps…. Write an equation of the line that passes through the point (-3, -5) and is parallel to the line y = 3x - 1 m = 3 - Step 1: what is the slope? - Step 2: To find the new y-intercept Plug the slope and given point into y = mx + b -5 = 3(-3) + b 4 = b -5 = -9 + b - Step 3: Write an equation. Use y = mx + b. y = 3x + 4

Other examples Write an equation of the line that passes through the point (-2,11) and is parallel to the line y = -x + 6. Then graph the lines to see if they’re parallel. m = -1 Parallel line – y = -x + 9 Write an equation of the line that passes through the point (-2,5) and is parallel to the line 2y = 4x - 6. Then graph the lines to see if they’re parallel. m = 2 Parallel line – y = 2x + 9

Perpendicular Lines If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. Perpendicular lines Slopes are negative reciprocals of each other When lines intersect they form a right angle i.e. Horizontal and vertical lines are perpendicular to each other

Examples of perpendicular

Are these equations perpendicular?
1. 2. 3. 4.

Determine whether these line are parallel or perpendicular.
Line a: y = 5x – Line b: x + 5y = 2 Line c: -10y – 2x = 9 Step 1: Put each equation into slope-intercept form Line a: y = 5x - 3 Line b: Line c: Which are parallel? Which are perpendicular? Perpendicular Line a & Line b; Line a & Line c Parallel Line b & Line c

Example Write an equation of the line that passes through (4,-5) and is perpendicular to the line y = 2x + 3. - Step 1: what is the slope? m = 2  Because the slopes of perpendicular lines are negative reciprocals, so your new slope must be -½. Plug the new slope and given point into y = mx + b -5 = -½(4) + b -3 = b -5 = -2 + b - Step 3: Write an equation. Use y = mx + b. y = -½x - 3

Is Line a perpendicular to Line b?
Other examples Is Line a perpendicular to Line b? Line a: 2y + x = -12 Line b: 2y = 3x - 9 Write an equation of the line that passes through (4,3) and is perpendicular to the line y = 4x – 7.

Homework For homework, you will be completing WS 4D.
We will go over any questions on it tomorrow before you turn it in.