SOLUTION: Decide whether the pair line is parallel, perpendicular or neither
{{{2x+5y=5}}}
{{{5x-2y=10}}}
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Question 227363: Decide whether the pair line is parallel, perpendicular or neither
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Decide whether the pair line is parallel, perpendicular or neither
Step 1. Two lines are parallel when they have the same slope and two lines are perpendicular when the product of their slopes is -1 or m1*m2=-1 where m1 is the slope of the first line and m2 is the slope of the line perpendicular to the first line.
Step 2. Put above pair of lines in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).
Step 3. Let's look at and put it in slope-intercept form using the following steps.
Subtract 2x from both sides of the equation
Divide by 5 to both sides of the equation
Step 4. The equation in slope-intercept form is with the slope {{m1=-2/5) and y-intercept
Step 5. Let's now look at equation and put it in slope-intercept form.
Add 2y-10 to both sides of the equation
Divide by 2 to both sides of the equation
or
Step 6. The equation in slope-intercept form is with a slope and y-intercept .
Step 7. The slopes in Step 4 and 6 are and . The product of their slopes . The means the lines are perpendicular.
Step 8. ANSWER: The two given lines are perpendicular.
The graphs of these lines are shown below:
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
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