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Line L passes through (-4,3) and line P is the graph of 5x-6y=24. if L is perendicular to P, what isthe slope intercept form equation of l

If any number in the equation is not an integer, enter it as a fraction in simplest form

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Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...
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The equation for Line P can be rearranged into slope/intercept form as:
y  = (5/6) x -4
Thus the slope of line P is   5/6.    Since Line L is perpendicular to line P, its slope is - (6/5)  .   This is the negative reciprocal rule.   Once the slope of Line L is known, the formula for a line with known slope and one known point comes into play.  For Line L
(y-3) =   -(6/5) ( x - (-4))      This can be rearranged as
 y =  -(6/5) x  - 9/5
So the slope of Line L  is  -(6/5)   and the y intercept is -9/5