Equation of the line

Question

Write an equation of the line perpendicular to the line 8x+15y=12 and containing the point (11,17) write the answer in standard form. 

Answer 1

Doing this the way mentioned previously, any Ax + By = C can be

 

written in slope-intercept form as   y = -(A/B)x + (C/B)

 

So the slope of the original line is -8/15.   The slope of the perpendicular line is the "negative reciprocal" - my students call it "the negative flip".  Flip the fraction.  Change the sign (negate it: + will become -, - will become +).   

 

The slope of the perpendicular line then is +15/8.     This means that -A/B = 15/8.  One of these is negative.  With Standard Notation, the coefficient of X is NEVER NEGATIVE, so the 8, which attaches to the "Y" is the negative one.

 

The standard notation answer is  15x - 8y = C

 

Now plug in the point (11, 17) and find C.  

 

15(11) - 8(17) = 29

 

 

Final answer is  15x - 8y = 29   for the equation of the perpendicular line that passes through (11, 17)