Parallel and Perpendicualr 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

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

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.

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: