SOLUTION: ( 7 ,1 ) and is perpendicular to the line 5 x + 2 y = 5 can be written in the form y = mx+b where m is -3.5 solve for b

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Question 801277: ( 7 ,1 ) and is perpendicular to the line 5 x + 2 y = 5 can be written in the form y = mx+b where m is -3.5 solve for b
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
This question seems to be a mixture of wording from two different problems. I cannot have much faith on my guess about what the problem was supposed to be, but I hope my answer helps anyway.
5+x+%2B+2+y+=+5 can be written in the form y+=+mx%2Bb as y=-2.5x%2B2.5.
That can be found by solving for y:
5x%2B2y=5 --> 2y=5-5x --> 0.5%282y%29=0.5%285-5x%29 --> y=2.5-2.5x
When the equation of a line is in such a form, the coefficient of x is the slope of the line.
So the slope of 5+x+%2B+2+y+=+5 is -2.5.

A line perpendicular to 5+x+%2B+2+y+=+5 must have a slope of
m=%28-1%29%2F%28-2.5%29 --> m=0.4

All lines perpendicular to 5+x+%2B+2+y+=+5 will have as an equation in the form y+=+mx%2Bb
an equation represented by y=0.4x%2Bb.

The one an only one of those lines perpendicular to 5+x+%2B+2+y+=+5 that passes through point (7,1) will have system+%28x=7%2Cy=1%29 as a solution to
y=0.4x%2Bb
So we will have
1=0.4%2A7%2Bb --> 1=2.8%2Bb --> b=1-2.8 --> b=-1.8
So the line perpendicular to 5+x+%2B+2+y+=+5 and passing through (7,1) has the equation y=0.4x-1.8.
The same equation can be written in many ways.
For example, multiplying both sides times 5 we get the equivalent equation
5y=2x-9.
And that can be transformed into the equivalent equations
2x-5y-9=0 and 2x-5y=9.