Parallel and perpendicular

 

Parallel and Perpendicular

 

Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment:

Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept form.

If your first name starts with

Write the equation of a line parallel to the given line but passing through the given point.

Write the equation of a line perpendicular to the given line but passing through the given point.

 

A or N

  

B or O

  

   

C or P

    

D or Q

    

E or R

    

F or S

    

G or T

    

H or U

    

I or V

    

J or W

    

K or X

    

L or Y

    

M or Z

    

Discuss the steps necessary to carry out each activity. Describe briefly what each line looks like in relation to the original given line.

 

Answer these two questions briefly in your own words:  

 

What does it mean for one line to be parallel to another? 

 

What does it mean for one line to be perpendicular to another?

 

Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): 

 

Origin  

 

Ordered pair  

 

X- or y-intercept   

 

Slope    

 

Reciprocal

 

My last name starts with a B

 

INSTRUCTORGUIDANCE EXAMPLE: Week Three Discussion

Parallel and Perpendicular

For this week’s discussion I am going to find the equations of lines that are parallel or

perpendicular to the given lines and which are passing through the specified point. First I

will work on the equation for the parallel line.

The equation I am given is y = -⅔ x + 2

The parallel line must pass through point (-6, -3)

I have learned that a line parallel to another line has the same slope as the other line, so

now I know that the slope of my parallel line will be -⅔. Since I now have both the

slope and an ordered pair on the line, I am going to use the point-slope form of a linear

equation to write my new equation.

y – y1 = m(x – x1) This is the general form of the point-slope equation

y – (-3) = -⅔[x – (-6)] Substituting in my known slope and ordered pair

y + 3 = -⅔x + (-⅔)6 Simplifying double negatives and distributing the slope

y = -⅔x – 4 – 3 Because (-⅔)6 = -4 and 3 is subtracted from both sides

y = -⅔x – 7 The equation of my parallel line!

This line falls as you go from left to right across the graph of it, the y-intercept is 7 units

below the origin, and the x-intercept is 10.5 units to the left of the origin.

Now I am ready to write the equation of the perpendicular line.

The equation I am given is y = -4x – 1

The perpendicular line must pass through point (0, 5)

I have learned that a line perpendicular to another line has a slope which is the negative

reciprocal of the slope of the other line so the first thing I must do is find the negative

reciprocal of –4.

The reciprocal of -4 is -¼ , and the negative of that is –(-¼) = ¼. Now I know my slope

is ¼ and my given point is (0, 5). Again I will use the point-slope form of a linear

equation to write my new equation.

y – y1 = m(x – x1)

y – 5 = ¼ (x – 0) Substituting in the slope and ordered pair

y – 5 = ¼ x The zero term disappears

y = ¼ x + 5 Adding 5 to both sides of the equation

The equation of my perpendicular line!

This line rises gently as you move from left to right across the graph. The y-intercept is

five units above the origin and the x-intercept is 20 units to the left of the origin.

[The answers to part d of the discussion will vary with students’ understanding.]