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Showing posts with label lines. Show all posts
Showing posts with label lines. Show all posts

Thursday, April 25, 2013

Interactive: Parallel Lines

Interactive Instructions: Move the green points to change m and see that parallel lines have the same slope. You can also move the orange line.

[ NOTESParallel Lines ]

Saturday, November 3, 2012

Parallel and Perpendicular Lines

Many of the problems that we will encounter in this section involve parallel or perpendicular lines.  To study this we must focus on the slopes of the lines.

InteractiveParallel Lines ]

There is notation that corresponds to these ideas, for example,
reads "m perpendicular".  To find the slope of the perpendicular line simply reciprocate the number and change the sign.

InteractivePerpendicular Lines ]

Find the corresponding perpendicular slope.
Of course, just use the same slope if you are asked to find the slope a parallel line.

Are the lines parallel, perpendicular or neither?
Find the slope of the line perpendicular.
Now we use these facts and the formula for equations of lines to find equations given certain geometric information. Recall,
Example: Find the equation of the line perpendicular to y = −1/4 x + 2 passing through the point (−1,−5).

This three step process using slope-intercept form always works. We could find this equation using point-slope form as well as demonstrated below.

Example: Find the equation of the line perpendicular to y = −1/4 x + 2 passing through the point (−1, −5).

Notice that the answer y = 4x − 1 is the same using either method.

Find the equation of the line. (Using slope-intercept form.)

Find the equation of the line. (Using point-slope form.)

Friday, November 2, 2012

Finding Linear Equations

Slope intercept form also allows us to easily find the equation of the line given the graph.  If you are given the slope and any point on the line you can find its equation by following the steps below:

Example: Find the equation of the line passing through (2, 3) with slope m = 1/2.

Step 1: Use y = mx + b and find m.
Step 2: Use the given point to find b.
Step 3: Put it all together using y = mx + b.
Alternatively, you can use point-slope form to answer the same question.
Substitute (2, 3) and slope m = 1/2  into the formula as follows:
Either method is valid and the answer is the equation.

Find the equation of the given line.