SOLUTION: write an equation in slope intercept form of a line with the following characteristics: perpendicular to the graph of 2x-3y=12 and passing through the point at (4,3).

Algebra ->  Linear-equations -> SOLUTION: write an equation in slope intercept form of a line with the following characteristics: perpendicular to the graph of 2x-3y=12 and passing through the point at (4,3).      Log On


   

Question 197698: write an equation in slope intercept form of a line with the following characteristics: perpendicular to the graph of 2x-3y=12 and passing through the point at (4,3).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y=12 Start with the given equation.


-3y=12-2x Subtract 2x from both sides.


-3y=-2x%2B12 Rearrange the terms.


y=%28-2x%2B12%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-2%29%2F%28-3%29%29x%2B%2812%29%2F%28-3%29 Break up the fraction.


y=%282%2F3%29x-4 Reduce.


We can see that the equation y=%282%2F3%29x-4 has a slope m=2%2F3 and a y-intercept b=-4.


Now to find the slope of the perpendicular line, simply flip the slope m=2%2F3 to get m=3%2F2. Now change the sign to get m=-3%2F2. So the perpendicular slope is m=-3%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=2%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=%28-3%2F2%29%28x-4%29 Plug in m=-3%2F2, x%5B1%5D=4, and y%5B1%5D=3


y-3=%28-3%2F2%29x%2B%28-3%2F2%29%28-4%29 Distribute


y-3=%28-3%2F2%29x%2B6 Multiply


y=%28-3%2F2%29x%2B6%2B3 Add 3 to both sides.


y=%28-3%2F2%29x%2B9 Combine like terms.


So the equation of the line perpendicular to 2x-3y=12 that goes through the point is y=%28-3%2F2%29x%2B9.


Here's a graph to visually verify our answer:
Graph of the original equation y=%282%2F3%29x-4 (red) and the perpendicular line y=%28-3%2F2%29x%2B9 (green) through the point .