SOLUTION: Give the equation of the line that is perpendicular to the line y = x+4 and passes through point (0, -1).

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Question 325447: Give the equation of the line that is perpendicular to the line y = x+4 and passes through point (0, -1).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=x%2B4 has a slope m=1 and a y-intercept b=4.


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


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


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


y--1=-1%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=-1


y%2B1=-1%28x-0%29 Rewrite y--1 as y%2B1


y%2B1=-x-1%28-0%29 Distribute


y%2B1=-x%2B0 Multiply


y=-x%2B0-1 Subtract 1 from both sides.


y=-x-1 Combine like terms.


So the equation of the line perpendicular to y=x%2B4 that goes through the point is y=-x-1.


Here's a graph to visually verify our answer:


Graph of the original equation y=x%2B4 (red) and the perpendicular line y=-x-1 (green) through the point .