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Question 221723: through (5,8), perpendicular to -7x+6y=13, determine the equation
Answer by brich(7)   (Show Source):
You can put this solution on YOUR website! start with -7x+6y=13 and solve for y:
start: (write the equation)
-7x+6y=13
step 1: (Add 7x to both sides)
6y=7x+13
step 2: (Divide both sides by 6)
y=(7/6)x+(13/6)
step 3: (Notice that the equation is now in slope-intercept form, y-mx+b)
m=7/6
b=13/6
step 4: (Recall that the line perpendicular to y=(7/6)x+(13/6) has a slope equal to the negative reciprocal of the slope of y=(7/6)x+(13/6))
m=7/6
m of perpendicular line = -6/7
step 5: (Set up the slope-intercept form equation, y=mx+b, of the perpendicular line using the new slope)
y=(-6/7)x+b
step 6: (Plug the point (5,8) into the new equation)
8=((-6/7)5)+b
step7: (simplify)
8=(-30/7)+b
step8: (Subtract (-30/7) from both sides to solve for b)
8+(30/7)=b
step9: (Find a common denominator and add)
(8)(7/7)+(30/7)=b
(56/7)+(30/7)=b
86/7=b
step10: (Substitute b into the equation of the perpendicular line)
y=(-6/7)x+b
y=(-6/7)x+(86/7)
step11: (Your finished, circle and state your answer)
y=(-6/7)x+(86/7)
I was very detailed in my description. I hope you understood it all. Please let me know if I was of help to you.
Bryan
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