Question 7792
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 = ".


{{{ 9x + 5y = 94 }}} <--- start here


{{{ 5y = 94 - 9x }}} <--- subtracted 9x from both sides


{{{ y = 94/5 - (9/5)x }}} <---- 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 {{{ (y - y[0]) = m(x - x[0]) }}} where m is your slope, and ({{{x[0]}}},{{{y[0]}}}) is a given point that the line goes through. Let's plug the values in:


{{{ (y - 8) = (5/9)(x - 6) }}} <--- now this needs some work so that we can put it in standard form


{{{ 9(y - 8) = 5(x - 6) }}} <---- multiply the whole equation by 9 to get rid of the fraction.


{{{ 9y - 72 = 5x - 30 }}} <---- used distributive property.


{{{ -5x + 9y = 42 }}} <---- 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.