Greetings and Happy Holidays!
<span>
1) Perpendicular to </span>
![-x+5y=14](https://tex.z-dn.net/?f=-x%2B5y%3D14)
In order for lines to be
perpendicular, their slopes must be
negative reciprocals.Example of slopes with negative reciprocals: 5 and
![\frac{-1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-1%7D%7B5%7D%20)
First,
rearrange the equation into
slope y-intercept form:
![-x+5y=14](https://tex.z-dn.net/?f=-x%2B5y%3D14)
![5y=x+14](https://tex.z-dn.net/?f=5y%3Dx%2B14)
![\frac{5y}{5}=\frac{x+14}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5y%7D%7B5%7D%3D%5Cfrac%7Bx%2B14%7D%7B5%7D%20)
![y=\frac{1}{5}x+\frac{14}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B5%7Dx%2B%5Cfrac%7B14%7D%7B5%7D)
The
slope of the equation is: \frac{1}{5}
The
negative reciprocal formula:
![(m_{1})(m_{2})=-1](https://tex.z-dn.net/?f=%20%28m_%7B1%7D%29%28m_%7B2%7D%29%3D-1)
Solve for the negative reciprocal:
Divide both sides by
![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
![\frac{\frac{1}{5}m_{2} }{ \frac{1}{5}} = \frac{-1}{ \frac{1}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B5%7Dm_%7B2%7D%20%7D%7B%20%5Cfrac%7B1%7D%7B5%7D%7D%20%3D%20%5Cfrac%7B-1%7D%7B%20%5Cfrac%7B1%7D%7B5%7D%7D)
![m_{2}=(-1)(\frac{5}{1})](https://tex.z-dn.net/?f=m_%7B2%7D%3D%28-1%29%28%5Cfrac%7B5%7D%7B1%7D%29)
![m_{2}=(\frac{-5}{1})](https://tex.z-dn.net/?f=m_%7B2%7D%3D%28%5Cfrac%7B-5%7D%7B1%7D%29)
![m_{2}=-5](https://tex.z-dn.net/?f=m_%7B2%7D%3D-5)
The slope of the new line is:
-5
2) Passes through (-5,-2)
Create an equation with the slope discovered in slope y-intercept form.
![y=-5x+b](https://tex.z-dn.net/?f=y%3D-5x%2Bb)
Input the point the line passes through.
![(-2)=-5(-5)+b](https://tex.z-dn.net/?f=%28-2%29%3D-5%28-5%29%2Bb)
Solve for b (the y-intercept).
![-2=-5(-5)+b](https://tex.z-dn.net/?f=-2%3D-5%28-5%29%2Bb)
Multiply.
![-2=25+b](https://tex.z-dn.net/?f=-2%3D25%2Bb)
Add -25 to both sides.
![(-2)+(-25)=b](https://tex.z-dn.net/?f=%28-2%29%2B%28-25%29%3Db)
![-27=b](https://tex.z-dn.net/?f=-27%3Db)
The y-intercept is equal to
-27
The Equation of the line is:
![y=-5x-27](https://tex.z-dn.net/?f=y%3D-5x-27)
I hope this helped!
-Benjamin
Answer:
Slope: -3
y-intercept: 1
Step-by-step explanation:
Answer:
68
Step-by-step explanation:
4 + (11 - 3)^2
= 4 + 8^2
= 4 + 64
= 68
37.................................
Answer:
1. One side of a rectangle is 4 in shorter than three times the other side. Find the sides if the
perimeter of the rectangle is 48 in.
Solution: Let us denote the shorter side by x: Then the other side is 3x
We now apply the zero property. Either x