Parallel and Perpendicualr Lines

Parallel and Perpendicular Lines

On graph paper, graph the following lines on one coordinate plane.
y = 1/2 x - 3
y = 1/2x + 4


On a new coordinate plane, graph the following lines together.
y = -2x + 1
y = -2x - 2

Open Ended

What do you notice about both sets of lines?

Open Ended

What part of the equation would support your previous answer?

Did you notice that these lines are parallel?

(I hope so!)

Did you notice that their slopes are equal to each other?


This is what makes them parallel.

On graph paper, graph the following lines on one coordinate plane.
y = 1/2 x - 2
y = -2 x + 2


On a new coordinate plane, graph the following lines together.
y = 2/3x + 1
y = -3/2x + 4

Open Ended

What do you notice about both sets of lines?

Open Ended

What do you notice about their slopes?

Did you notice that these lines are perpendicular to each other?





You should have noticed that their slopes are the negative reciprocal of each other. If you multiplied their slopes, the product would be -1.

Match

Match the following perpendicular slopes.

(negative reciprocals of each other)

• 6
• -6
• 1/3

• -2

• 3

-1/6

1/6

-1/3

1/2

-3

• -1/6
• 1/6

• -1/3

• 1/2

• -3

Multiple Choice

Are these lines parallel, perpendicular, or neither?

y = 1/3x + 6

y = - 1/3x + 4

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are these lines parallel, perpendicular, or neither?

y = 1/3x + 6

y = - 1/3x + 4

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are these lines parallel, perpendicular, or neither?

y = 1/4x + 2

y = -4x + 5

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are these lines parallel, perpendicular, or neither?

x + 4y = -8

12x - 3y = -3

(Hint: Lines should be in slope-intercept form)

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are these lines parallel, perpendicular, or neither?

2x + 3y = 5

6x - 9y = 21

(Hint: Lines should be in slope-intercept form)

• Parallel

• Perpendicular

• Neither

Step 1: Identify slope. m = 3
Step 2: Plug into Point-Slope Form
y + 5 = 3(x + 3)
Step 3: Change equation into Slope-Intercept form
y + 5 = 3x + 9
y = 3x + 4

​Option 2:

Step 1: Identify slope. m = 3
Step 2: Calculate the y-intercept
-5 = 3(-3) + b
-5 = -9 + b
4 = b
Step 3: Write the Equation.
y= 3x + 4

​Option 1:

Write an equation in slope-intercept form of the line that is parallel to
y = 3x + 1 that passes through (-3, -5).
Copy both options into your notebook. You can use whichever one you like best.

Multiple Choice

Write the equation of the line that is parallel to y = 2x + 1

that passes through (-1, 1)

• y = -1/2x + 1

• y = 2x + 1

• y = 2x + 3

• y = 2x - 1

Multiple Choice

Write the equation of the line that is perpendicular to y = 1/2x - 9

that passes through (7, 10)

• y = -2x + 24

• y = 2x + 1

• y = -2x - 24

• y = -1/2x - 1