SOLUTION: What is the equation of the line that passes through the given point and is perpendicular to the given line?
(8,-1), 4y + 2x = 12
i got y= -2x-3.
I tried my best, but
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Question 174200: What is the equation of the line that passes through the given point and is perpendicular to the given line?
(8,-1), 4y + 2x = 12
i got y= -2x-3.
I tried my best, but didn't quite understand the problem, so it would be great if you could check my answer. Thankyou so much!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.
Subtract from both sides.
Rearrange the terms.
Divide both sides by to isolate y.
Break up the fraction.
Reduce.
We can see that the equation has a slope and a y-intercept .
Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .
Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point )
.
Start with the point slope formula
Plug in , , and
Rewrite as
Distribute
Multiply
Subtract 1 from both sides.
Combine like terms.
So the equation of the line perpendicular to that goes through the point is .
Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point .
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