Free counters!

Wednesday, May 8, 2013

Equation - Perpendicular Lines

Category: Analytic Geometry, Algebra

"Published in Newark, California, USA"

Find the equation of a line that passes through the point (2, -1) and perpendicular to the line 2x - 3y + 4 = 0.

Solution:

Consider the given line



Rewrite the equation of a line in slope-intercept form as follows







The slope of a line is m1 = 2/3 and the y-intercept is b = 4/3. To draw or sketch a line, plot  4/3 at the y-axis. This is your first point of the line at (0, 4/3). Next, use the slope to get the second point. From the first point, count 3 units to the right and then 2 units upward. Connect the two points and you have now a line as follows


Photo by Math Principles in Everyday Life

Finally, plot (2, -1) and draw a line perpendicular to the given line that contains a given point as follows


Photo by Math Principles in Everyday Life

If two lines are perpendicular, then their slopes are negative reciprocals to each other which means that m2 = -1/m1 = -3/2. Therefore, using the point-slope form, the equation of another line that passes through the point (2, -1) is