SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line? (2,9)8x+y=4 and (5,-9)4x+7y=8

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line? (2,9)8x+y=4 and (5,-9)4x+7y=8      Log On


   

Question 312669: Write an equation of the line containing the given point and perpendicular to the given line?
(2,9)8x+y=4 and (5,-9)4x+7y=8
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that perpendicular lines have slopes that are negative reciprocals of each other.

First, let's find the slope of the line. Do this by rearranging the equation so that it is in y=mx+b form.
8x+y=4
y=-8x+4

The slope is -8. The negative reciprocal of -8 is 1/8. The perpendicular line therefore has a slope of 1/8.

Now use this slope, and the point x=2, y=9, in the y=mx+b equation to solve for b:
y=mx+b
9=(1/8)2+b
9=2/8 + b
9-1/4 = b
36/4 - 1/4 = b
35/4 = b

The equation of the line is y=(1/8)x + 35/4


For the second question, do the same thing. Find the perpendicular slope, it's 7/4

Then use x=5 and y=-9 to solve for b:
You should find this equation: y=(7/4)x -71/4