SOLUTION: Write the equation in slope-intercept form for the line through (-2, 6) and perpendicular to 2x-3y=5

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Question 243011: Write the equation in slope-intercept form for the line through (-2, 6) and perpendicular to 2x-3y=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y=5 Start with the given equation.


-3y=5-2x Subtract 2x from both sides.


-3y=-2x%2B5 Rearrange the terms.


y=%28-2x%2B5%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-2%29%2F%28-3%29%29x%2B%285%29%2F%28-3%29 Break up the fraction.


y=%282%2F3%29x-5%2F3 Reduce.


We can see that the equation y=%282%2F3%29x-5%2F3 has a slope m=2%2F3 and a y-intercept b=-5%2F3.


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=-3%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-6=%28-3%2F2%29%28x--2%29 Plug in m=-3%2F2, x%5B1%5D=-2, and y%5B1%5D=6


y-6=%28-3%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-6=%28-3%2F2%29x%2B%28-3%2F2%29%282%29 Distribute


y-6=%28-3%2F2%29x-3 Multiply


y=%28-3%2F2%29x-3%2B6 Add 6 to both sides.


y=%28-3%2F2%29x%2B3 Combine like terms.


So the equation of the line perpendicular to 2x-3y=5 that goes through the point is y=%28-3%2F2%29x%2B3.


Here's a graph to visually verify our answer:


Graph of the original equation y=%282%2F3%29x-5%2F3 (red) and the perpendicular line y=%28-3%2F2%29x%2B3 (green) through the point .