SOLUTION: Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12 .

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Question 225051: Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12 .

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12.

Step 1. Two lines are perpendicular if their product of the slopes is -1. In equation form m1*m2=-1 where m1 is the slope given by the first equation. And m2 is the slope of the line perpendicular to the first line.

Step 2. We need to put the above given line in slope intercept form so we can find the slope of the given line. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b).

Step 3. The following steps puts the above equation in slope-intercept form

11x%2B55y=-12

Subtract 11 from both sides of the equation

11x%2B55y-11x=-12-11x

55y=-11x-12

Divide by 5 to both sides of the equation

55y%2F55=-11x%2F55-12%2F55

y=-x%2F5-12%2F55

Step 4. Comparing the last equation with y=mx+b, the slope m1=-1/5.

Step 5. Therefore, the slope of the perpendicular line is m2=-1%2F%28-1%2F5%29=5 since the product of the slopes between the two lines is -1 (or m1*m2=-1)

Step 6. So now we have a perpendicular line with slope m2=5 that must pass through the point (4,25)

Step 7. Given two points (x1,y1) and (x2,y2), then the slope m is given as

m=%28y2-y1%29%2F%28x2-x1%29

Step 4. Let (x1,y1)=(4,25) or x1=4 and y1=25. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=5. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

5=%28y-25%29%2F%28x-4%29%29

Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.

5%28x-4%29=%28x-4%29%28y-25%29%2F%28x-4%29

5x-20=y-25

Add 25 to both sides of the equation

5x-20%2B25=y-25%2B25

5x%2B5=y

Step 7. ANSWER: The equation of the perpendicular line in slope-intercept form is y=5x%2B5

And the graph of the two lines are shown below.

graph%28600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+5x%2B5%2C-x%2F5-12%2F55%29

I hope the above steps and explanation 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