SOLUTION: what is the equation in slope intercept form of a line perpendicular to 5y+3x=7 that goes through the point (-2,6)

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Question 345143: what is the equation in slope intercept form of a line perpendicular to 5y+3x=7 that goes through the point (-2,6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5y%2B3x=7 Start with the given equation.


5y=7-3x Subtract 3x from both sides.


5y=-3x%2B7 Rearrange the terms.


y=%28-3x%2B7%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28%28-3%29%2F%285%29%29x%2B%287%29%2F%285%29 Break up the fraction.


y=-%283%2F5%29x%2B7%2F5 Reduce.


We can see that the equation y=-%283%2F5%29x%2B7%2F5 has a slope m=-3%2F5 and a y-intercept b=7%2F5.


Now to find the slope of the perpendicular line, simply flip the slope m=-3%2F5 to get m=-5%2F3. Now change the sign to get m=5%2F3. So the perpendicular slope is m=5%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=5%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-6=%285%2F3%29%28x--2%29 Plug in m=5%2F3, x%5B1%5D=-2, and y%5B1%5D=6


y-6=%285%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-6=%285%2F3%29x%2B%285%2F3%29%282%29 Distribute


y-6=%285%2F3%29x%2B10%2F3 Multiply


y=%285%2F3%29x%2B10%2F3%2B6 Add 6 to both sides.


y=%285%2F3%29x%2B28%2F3 Combine like terms.


So the equation of the line perpendicular to 3x%2B5y=7 that goes through the point is y=%285%2F3%29x%2B28%2F3.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%283%2F5%29x%2B7%2F5 (red) and the perpendicular line y=%285%2F3%29x%2B28%2F3 (green) through the point .