SOLUTION: I tried to start it, but I really don't know what to do!? Write the slope for a perpendicular line. 2x+4y=8 and I have one more question if it's not to much. Find the equation of t

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Question 214284: I tried to start it, but I really don't know what to do!? Write the slope for a perpendicular line. 2x+4y=8 and I have one more question if it's not to much. Find the equation of the line that is perpendicular to the line y=-1/3x+5 and goes through the point (1,2). -1/3 is a fraction thanks!!
Found 2 solutions by drj, solver91311:
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
I tried to start it, but I really don't know what to do!? Write the slope for a perpendicular line. 2x+4y=8 and I have one more question if it's not to much. Find the equation of the line that is perpendicular to the line y=-1x/3+5 and goes through the point (1,2). -1/3 is a fraction thanks!!

Step 1. Let's put 2x+4y=8 in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept. The y-intercept occurs when x=0 or at point (0,b)



Divide by 2 to both sides of the equation





Subtract x from both sides of equation to get y term by itself on left side.





Divide by 2 to both sides of equation to get y





Step 2. So the slope for the last equation is and the y-intercept is 2.

Step 3. Now, two lines are perpendicular when the product of their slopes equal to -1. Since the slope is -1/2 and then the line perpendicular to this line is 2. That is,
or

Step 4. ANSWER. The slope of a line perpendicular to is m=2.

Step 5. Now, let's find the equation of the line that is perpendicular to the line y=-1x/3+5 and goes through the point (1,2).

Step 6. Now based on the previous steps, we know that the slope for this line is -1/3 then the slope of a line perpendicular to it is 3 or m=3.

Step 7. The perpendicular line needs to pass through point (1,2) or x=1 and y=2. So far the equation of the line is y=3x+b. Substitute x=1 and y=2 into the equation to get b.







Step 8. ANSWER. The equation is then y=3x-1 where m=3 is the slope and b=-1 is the y-intercept.
Here's a graph of the two perpendicular lines:



Note the perpendicular line passes through point (1,2). The equation for the green perpendicular line is y=3x-1 and the equation for the red line is y=-x/3+5. Note the y-intercept for both lines.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

The slopes of two lines perpendicular to each other are negative reciprocals.



Write your equation in slope-intercept form, that is, solve for so it looks like this: . The part will be the slope. Take the negative of the reciprocal of that slope and you will have the slope of any line perpendicular to the given line.

In your second problem, your given equation is already in slope-intercept form and we can see that the slope of that line is . The reciprocal of is -3 and the negative of that is 3, so we know that the slope of the desired line is 3. Now use the point-slope form of a line to derive the desired equation:



Where is the slope and is the given point. Just substitute what you know:



Now you can put it into whatever form your instructor requires -- or just leave it like it is.

John
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