Answer:
![y = -\frac{3}{2}x -1](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%20-1)
Step-by-step explanation:
Given
Perpendicular to ![y = \frac{2}{3}x + 2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%20%2B%202)
Pass through ![(-2,2)](https://tex.z-dn.net/?f=%28-2%2C2%29)
Required
Determine the line equation
First, we need to determine the slope of ![y = \frac{2}{3}x + 2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%20%2B%202)
An equation is of the form:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where
![m = slope](https://tex.z-dn.net/?f=m%20%3D%20slope)
In this case:
![m = \frac{2}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
Next, we determine the slope of the second line.
Since both lines are perpendicular, the second line has a slope of:
![m_1 = \frac{-1}{m}](https://tex.z-dn.net/?f=m_1%20%3D%20%5Cfrac%7B-1%7D%7Bm%7D)
![m_1 = \frac{-1}{2/3}](https://tex.z-dn.net/?f=m_1%20%3D%20%5Cfrac%7B-1%7D%7B2%2F3%7D)
![m_1 = -\frac{3}{2}](https://tex.z-dn.net/?f=m_1%20%3D%20-%5Cfrac%7B3%7D%7B2%7D)
Since this line passes through (-2,2); The equation is calculated as thus:
![y - y_1 = m_1(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m_1%28x%20-%20x_1%29)
Where
![(x_1,y_1) = (-2,2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-2%2C2%29)
This gives:
![y - 2 = -\frac{3}{2}(x - (-2))](https://tex.z-dn.net/?f=y%20-%202%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x%20-%20%28-2%29%29)
![y - 2 = -\frac{3}{2}(x +2)](https://tex.z-dn.net/?f=y%20-%202%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x%20%2B2%29)
![y - 2 = -\frac{3}{2}x -3](https://tex.z-dn.net/?f=y%20-%202%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%20-3)
Add 2 to both sides
![y - 2+2 = -\frac{3}{2}x -3 + 2](https://tex.z-dn.net/?f=y%20-%202%2B2%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%20-3%20%2B%202)
![y = -\frac{3}{2}x -1](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%20-1)
Answer:
4091
Step-by-step explanation:
Given the equation;
3x + 7x − 28 + 31 − 8x
First, we would collect like terms;
3x + 7x − 8x − 28 + 31
Simplifying, we have;
For x = 2043;
2(2043) + 5 = 4086 + 5 = 4091.
Standard form of linear eqn : y=mx+c
m= gradient
c= y intercept
Line that is parallel = Same Gradient
Eqn of 2nd Line : y=0.75x+c
Given (8,0) where x=8 and y =0,
0=(0.75)(8) + c
c = -6
Therefore y=0.75x-6
Answer:
dbbxnxnznndn
Step-by-step explanation:
hdhhdhdhdjxmdk