SOLUTION: What is the equation for a line that passes through (6,8) and is perpendicular to 9x+5y=94?

Question 7792: What is the equation for a line that passes through (6,8) and is perpendicular to 9x+5y=94?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
They give you the line 9x + 5y = 94, right? If you want to find the slope of the line perpendicular to the line given to you, you must first find the slope of the line given to you.

9x + 5y = 94 needs some work. We need to change that around until we get it to say "y = ".

<--- start here

<--- subtracted 9x from both sides

<---- divide both sides by 5 so that the y can be alone finally. The -9/5 would be the slope of the line given to you.

Now, the slope of the perpendicular is ALWAYS the negative (or opposite) reciprocal. If your slope is -9/5, then the opposite reciprocal will be 5/9. What you do is to flip the fraction and change the sign.

Now, we know that the slope of the perpendicular line will be 5/9. They're given us some additional information. The perpendicular line passes through the point (6,8). There is a formula that exists that we can plug in the slope and a point. That would be where m is your slope, and (,) is a given point that the line goes through. Let's plug the values in:

<--- now this needs some work so that we can put it in standard form

<---- multiply the whole equation by 9 to get rid of the fraction.

<---- used distributive property.

<---- moved the 5x to the left (as it became -5x) and added 72 to both sides. This is now our equation in standard form. This is the equation of the line perpendicular to 9x+5y=94.
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