Parallel and Perpendicular Lines
The Canadian Museum of Civilization
_
This museum has a lot of parallel and perpendicular lines in the building. Do you see them?
Parallel Lines have the same slope. If you know a point on the line or the y-intercept and another line it is parallel to, you can write the equation.
Write the equation of the line parallel to y = 3x - 2 and crossing the y-axis at (0, -1). From y = 3x - 2, we can tell m = 3. Since parallel lines have the same slope, the slope of the parallel line also equals 3. We can see that our point is the y-intercept, so b= -1. Substituting those values into the Slope-Intercept Form of a line:
y = mx + b
y = 3x - 1
Perpendicular Lines have opposite reciprocals for slopes. Opposite reciprocals are two fractions that have opposite signs and one fraction is the reciprocal (or flipped) of the other. If a line has a slope of 2/3, then the perpendicular line will have a slope of -3/2.
What is the slope of the line that is perpendicular to y = 5x - 18?
The slope of y = 5x - 18 is 5. The opposite reciprocal to 5 is -1/5. So, the slope of the line parallel to y = 5x - 18 is -1/5.
PRACTICE
Try to do these problems then click on "Step 2" to see if you did them correctly: http://www.flvs.net/areas/studentservices
/eoc/algebra-review/module10/10_18a_d_c.htm
ASSESS
Test yourself using the interactive assessment on the bottom of this website: http://www.algebralab.org/lessons
/lesson.aspx?file=geometry_coordparallelperpendicular.xml
When you are done, try this quiz: http://www.media.pearson.com.au
/schools/cw/au_sch_bull_gm12_1/dnd/3_para.html
Now that you can write any linear equation, go back to the Writing Linear Equations page and do the problems listed there.
This museum has a lot of parallel and perpendicular lines in the building. Do you see them?
Parallel Lines have the same slope. If you know a point on the line or the y-intercept and another line it is parallel to, you can write the equation.
Write the equation of the line parallel to y = 3x - 2 and crossing the y-axis at (0, -1). From y = 3x - 2, we can tell m = 3. Since parallel lines have the same slope, the slope of the parallel line also equals 3. We can see that our point is the y-intercept, so b= -1. Substituting those values into the Slope-Intercept Form of a line:
y = mx + b
y = 3x - 1
Perpendicular Lines have opposite reciprocals for slopes. Opposite reciprocals are two fractions that have opposite signs and one fraction is the reciprocal (or flipped) of the other. If a line has a slope of 2/3, then the perpendicular line will have a slope of -3/2.
What is the slope of the line that is perpendicular to y = 5x - 18?
The slope of y = 5x - 18 is 5. The opposite reciprocal to 5 is -1/5. So, the slope of the line parallel to y = 5x - 18 is -1/5.
PRACTICE
Try to do these problems then click on "Step 2" to see if you did them correctly: http://www.flvs.net/areas/studentservices
/eoc/algebra-review/module10/10_18a_d_c.htm
ASSESS
Test yourself using the interactive assessment on the bottom of this website: http://www.algebralab.org/lessons
/lesson.aspx?file=geometry_coordparallelperpendicular.xml
When you are done, try this quiz: http://www.media.pearson.com.au
/schools/cw/au_sch_bull_gm12_1/dnd/3_para.html
Now that you can write any linear equation, go back to the Writing Linear Equations page and do the problems listed there.