Geometry Equations of Parallel and Perpendicular Lines

Instructions

You must show your work or explain your answer on each problem to receive credit.  Graphing the points and lines in Desmos is a great way to check your work, however this does not count as work.

Write equations of parallel and perpendicular lines in slope-intercept form.


Slope:  How steep the line is, rise/run.  The 'm' value in y = mx + b.
Parallel Lines:  Two lines with the same slope, will never meet
Perpendicular Lines:  Two lines with negative reciprocal (flip the fraction) slopes, form a right angle at their intersection

1

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

1

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

1

Tell whether line 1 and line 2 through the given points are parallel, perpendicular or neither. Show your work finding each slope or explain your answer. (This must be shown or explained mathematically, a Desmos screenshot does not count as work. Desmos is a great tool to check your work!)
Line 1: (0, 3), (6, -5)
Line 2: (-2, 2), (6,8)

Parallel

Perpendicular

Neither

1

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-1,3), y=4x-7

1

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-8,6), y=-4x-1

1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(6,10), y=-3x+13

1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(-20,4), y=(-2/5)x+2

1

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe. Show your work.

1

Your friend claims that if a line has a slope that is less than 1, then any line perpendicular to it must have a positive slope. Is your friend correct? Explain your reasoning.

Check your work so far using the answers posted in Google Classroom.  Then complete the following exit ticket problems.   Show all of your work!

1

Tell whether line 1 and line 2 are parallel, perpendicular or neither. Show your work finding each slope or explain your answer.
Line 1: (-1,-6), (4, 2)
Line 2: (-2, 1), (0, 2)

Parallel

Perpendicular

Neither

1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(0,-8), y=(-1/3)x-10

1

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(2,-3), y=-6x+10

1

EXTENSION: Write an equation of a line that is parallel to the line 4x+3y=36 and passes through the point (1,5).

1

Rate your understanding on writing equations of parallel and perpendicular lines.

1-Beginning

2-Approaching

3-Mastery

4-Advanced (Completed the extension problems)

Geometry Equations of Parallel and Perpendicular Lines

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(-1,3), y=4x-7

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(-8,6), y=-4x-1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(6,10), y=-3x+13

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(-20,4), y=(-2/5)x+2

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe. Show your work.

Your friend claims that if a line has a slope that is less than 1, then any line perpendicular to it must have a positive slope. Is your friend correct? Explain your reasoning.

Tell whether line 1 and line 2 are parallel, perpendicular or neither. Show your work finding each slope or explain your answer.Line 1: (-1,-6), (4, 2)Line 2: (-2, 1), (0, 2)

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(0,-8), y=(-1/3)x-10

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(2,-3), y=-6x+10

EXTENSION: Write an equation of a line that is parallel to the line 4x+3y=36 and passes through the point (1,5).

Rate your understanding on writing equations of parallel and perpendicular lines.

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

Graph the following two equations in desmos. What do you notice? What are their slopes? Are they parallel or perpendicular? www.desmos.com/calculator

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(-1,3), y=4x-7

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(-8,6), y=-4x-1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(6,10), y=-3x+13

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(-20,4), y=(-2/5)x+2

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe. Show your work.

Your friend claims that if a line has a slope that is less than 1, then any line perpendicular to it must have a positive slope. Is your friend correct? Explain your reasoning.

Tell whether line 1 and line 2 are parallel, perpendicular or neither. Show your work finding each slope or explain your answer.Line 1: (-1,-6), (4, 2)Line 2: (-2, 1), (0, 2)

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.P(0,-8), y=(-1/3)x-10

Write an equation of the line passing through point P that is parallel to the given line. Show your work.P(2,-3), y=-6x+10

EXTENSION: Write an equation of a line that is parallel to the line 4x+3y=36 and passes through the point (1,5).

Rate your understanding on writing equations of parallel and perpendicular lines.

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-1,3), y=4x-7

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-8,6), y=-4x-1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(6,10), y=-3x+13

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(-20,4), y=(-2/5)x+2

Tell whether line 1 and line 2 are parallel, perpendicular or neither. Show your work finding each slope or explain your answer.
Line 1: (-1,-6), (4, 2)
Line 2: (-2, 1), (0, 2)

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(0,-8), y=(-1/3)x-10

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(2,-3), y=-6x+10

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-1,3), y=4x-7

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(-8,6), y=-4x-1

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(6,10), y=-3x+13

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(-20,4), y=(-2/5)x+2

Tell whether line 1 and line 2 are parallel, perpendicular or neither. Show your work finding each slope or explain your answer.
Line 1: (-1,-6), (4, 2)
Line 2: (-2, 1), (0, 2)

Write an equation of the line passing through point P that is perpendicular to the given line. Show your work.
P(0,-8), y=(-1/3)x-10

Write an equation of the line passing through point P that is parallel to the given line. Show your work.
P(2,-3), y=-6x+10