SOLUTION: Write the equation of the line perpendicular to 9x + 2y = 18 and passes through the point (1, 4).

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Question 199963: Write the equation of the line perpendicular to 9x + 2y = 18 and passes through the point (1, 4).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%2B2y=18 Start with the given equation.


2y=18-9x Subtract 9x from both sides.


2y=-9x%2B18 Rearrange the terms.


y=%28-9x%2B18%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-9%29%2F%282%29%29x%2B%2818%29%2F%282%29 Break up the fraction.


y=-%289%2F2%29x%2B9 Reduce.


We can see that the equation y=-%289%2F2%29x%2B9 has a slope m=-9%2F2 and a y-intercept b=9.


Now to find the slope of the perpendicular line, simply flip the slope m=-9%2F2 to get m=-2%2F9. Now change the sign to get m=2%2F9. So the perpendicular slope is m=2%2F9.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-9%2F2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-4=%282%2F9%29%28x-1%29 Plug in m=2%2F9, x%5B1%5D=1, and y%5B1%5D=4


y-4=%282%2F9%29x%2B%282%2F9%29%28-1%29 Distribute


y-4=%282%2F9%29x-2%2F9 Multiply


y=%282%2F9%29x-2%2F9%2B4 Add 4 to both sides.


y=%282%2F9%29x%2B34%2F9 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 9x%2B2y=18 that goes through the point is y=%282%2F9%29x%2B34%2F9.


If you want the equation in standard form, then the equation is 2x-9y=34


Here's a graph to visually verify our answer:
Graph of the original equation y=-%289%2F2%29x%2B9 (red) and the perpendicular line y=%282%2F9%29x%2B34%2F9 (green) through the point .