parallel and perpendicular lines. warm – up!! * as you walk in, please pick up a calculator and...
DESCRIPTION
Before We Jump In…. A Quick Review! What is the Slope Intercept form? Y = mx + b Which variable is the slope and which is the y – intercept? M = slope and b = y-intercept Find the slope from the given equations. Example 1) y = -2x + 3Example 2) y = -5x – 7 Example 3) 4y = 8x – 12 Example 4) -10x + 5y = 25TRANSCRIPT
Parallel and Perpendicular Lines
Warm – up!! * As you walk in, please pick up a calculator and begin working on your warm –up!
1. What is the formula to find the midpoint?
2. What is the formula to find distance?
3. Find the midpoint of (5, 8) and (3, 6).
4. Find the distance between (3, 4) and (7, 4).
Before We Jump In…. A Quick Review! What is the Slope Intercept form? Y = mx + b
Which variable is the slope and which is the y – intercept? M = slope and b = y-intercept
Find the slope from the given equations. Example 1) y = -2x + 3 Example 2) y = -5x – 7 Example 3) 4y = 8x – 12 Example 4) -10x + 5y = 25
You Try!Find the slope.A) -36x + 6y = 72 B) y = 9x – 1
Graphing Equations
Ex. 1) y = -x + 3 Ex. 2) 6x – 2y = 12
Parallel SlopesEx. 1) y = 3x + 4 Ex. 2) y = -4x + 2
y = 3x – 2 -2y = 8x + 10
Parallel Slopes Continued ….After graphing these parallel lines, what do you notice about each set of equations?
• The slopes (m) in each equation are the same.
• The y – intercepts (b) are different.
Perpendicular SlopesEx. 1) Ex. 2) 2y – 8 = 5x 2y = -5x + 6 -2x – 8 = 5y
Perpendicular Slopes ContinuedAfter graphing these perpendicular lines, what do you notice about each set of equations?
• The slopes (m) in each equation are the negative reciprocal.
• The y – intercepts (b) are the same.
What can we conclude about Parallel Lines and Perpendicular Lines? Finding SlopeWhat is the equation to find slope? m = Given two lines, determine if the lines passing through the points are parallel, perpendicular, or neither. Examples-1. Line 1: (1, 2) and (3, 1) 2. Line 1: (0, 3) and (3, 1) Line 2: (0, -1) and (2, 0) Line 2: (-1, 4) and (-7, -5)
You Try! Example 3) Line 1: (2, -1) and (5, -7)Line 2: (0, 0) and (-1, 2)
More Examples:
Determine if the following lines are parallel, perpendicular, or neither. 1. 12x + 3y = -9 2. y = -5x + 12 3. -2y = 4 – x -8x – 2y = 14 5y = x – 15 2x – 4y = 12
4. Line 1: (1, 0) and (2, 0) 6. Line 1: (2, 5) and (-2, 7) Line 2: (5, -5) and (-10, -5) Line 2: (0, 4) and (1, 6)
Begin working on your practice!!