SOLUTION: write slope intercept form of the equation of a line passing through (-4,3) and perpendicular to line whose equation is y=1/3x-4

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Question 193269: write slope intercept form of the equation of a line passing through (-4,3) and perpendicular to line whose equation is y=1/3x-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can see that the equation y=%281%2F3%29x-4 has a slope m=1%2F3 and a y-intercept b=-4.


Now to find the slope of the perpendicular line, simply flip the slope m=1%2F3 to get m=3%2F1. Now change the sign to get m=-3. So the perpendicular slope is m=-3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=1%2F3 and the coordinates of the given point .


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


y-3=-3%28x--4%29 Plug in m=-3, x%5B1%5D=-4, and y%5B1%5D=3


y-3=-3%28x%2B4%29 Rewrite x--4 as x%2B4


y-3=-3x%2B-3%284%29 Distribute


y-3=-3x-12 Multiply


y=-3x-12%2B3 Add 3 to both sides.


y=-3x-9 Combine like terms.


So the equation of the line perpendicular to -x%2B3y=-12 that goes through the point is y=-3x-9.


Here's a graph to visually verify our answer:


Graph of the original equation y=%281%2F3%29x-4 (red) and the perpendicular line y=-3x-9 (green) through the point .