Answer:
Option 3 - ![y=-6x+28](https://tex.z-dn.net/?f=y%3D-6x%2B28)
Step-by-step explanation:
Given : Perpendicular to the line
; containing the point (4,4).
To Find : An equation for the line with the given properties ?
Solution :
We know that,
When two lines are perpendicular then slope of one equation is negative reciprocal of another equation.
Slope of the equation ![x - 6y = 8](https://tex.z-dn.net/?f=x%20-%206y%20%3D%208)
Converting into slope form
,
Where m is the slope.
![y=\frac{x-8}{6}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx-8%7D%7B6%7D)
![y=\frac{x}{6}-\frac{8}{6}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7B6%7D-%5Cfrac%7B8%7D%7B6%7D)
The slope of the equation is ![m=\frac{1}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B6%7D)
The slope of the perpendicular equation is ![m_1=-\frac{1}{m}](https://tex.z-dn.net/?f=m_1%3D-%5Cfrac%7B1%7D%7Bm%7D)
The required slope is ![m_1=-\frac{1}{\frac{1}{6}}](https://tex.z-dn.net/?f=m_1%3D-%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B6%7D%7D)
![m_1=-6](https://tex.z-dn.net/?f=m_1%3D-6)
The required equation is ![y=-6x+c](https://tex.z-dn.net/?f=y%3D-6x%2Bc)
Substitute point (x,y)=(4,4)
![4=-6(4)+c](https://tex.z-dn.net/?f=4%3D-6%284%29%2Bc)
![4=-24+c](https://tex.z-dn.net/?f=4%3D-24%2Bc)
![c=28](https://tex.z-dn.net/?f=c%3D28)
Substitute back in equation,
![y=-6x+28](https://tex.z-dn.net/?f=y%3D-6x%2B28)
Therefore, The required equation for the line is ![y=-6x+28](https://tex.z-dn.net/?f=y%3D-6x%2B28)
So, Option 3 is correct.
To establish this equation we first need to assign some variables.
Let us assign x as the number of hours he has worked
and assign y as the total amount of money that he has earned
Therefore the equation y=36.50x is the equation that correctly represents how much money he makes regardless of how many hours he works. Just plug in how many hours you want for x and then solve the equation and you will get how much money he makes in x amount of hours. This is also proportional because for every hour that he works he gets the same salary of 36.50. It is proportional because no matter how many hours he works the salary will go up the same amount for each extra hour he works. The proportion is 36.50 dollars per hour worked.
Answer:
Step-by-step explanation:
Petra