Answer:
y=4/3x-38/3
Explanation:
Equation: y=-3/4x-7
Change the reciprocal (x-value):
In order to change the reciprocal you must change the sign from negative to positive
-3/4 ---> 3/4
Then you must flip the fraction.
3/4 ---> 4/3
Adding in the given coordinates:
We must use the given coordinate in order to find the new y-intercept because '-7' is part of the perpendicular line of the new line we are creating.
In order to add in the given coordinates you must use 'y-y1=m(x-x1)' to get your new y-intercept.
The 'y' stays as 'y'
The 'y1' is the y-value of your coordinate
The 'm' is your new slope
The 'x' stays as 'x'
The 'x1' is the x-value of your coordinate
Coordinate Given: (5,-6) New Slope: 4/3
y-(-6)=(4/3)(x-(5))
To solve you must get 'y' by itself, so lets work on 'y-(-6)'.
A negative and a negative make a positive.
y-(-6) ---> y+6
Now let's work on '(4/3)(x-(5))'.
You must distribute in the 4/3
(4/3)(x) ---> 4/3x
(4/3)(-5) ---> -20/3
Now you have 'y+6=4/3x-20/3'
Now solve to get 'y' by itself by subtracting 6 on both sides.
y+6 -6 ---> y (the 6's cancel out)
4/3x-20/3 -6 ---> 4/3x-38/3 (You only subtract the same number and since there was no 'x' you can only subtract 6 from (-20/3))
So now you have your new line that is perpendicular to your first line
New Equation: y=4/3x-38/3