![m = \frac{4-16}{-6-6} \\m = \frac{-12}{-12} \\\\m = 1](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4-16%7D%7B-6-6%7D%20%5C%5Cm%20%3D%20%5Cfrac%7B-12%7D%7B-12%7D%20%5C%5C%5C%5Cm%20%3D%201)
Therefore, the slope of the line is 1. In case if you want to know the equation.
![y=mx+b\\y=x+b\\4=-6+b\\4+6=b\\10=b\\](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3Dx%2Bb%5C%5C4%3D-6%2Bb%5C%5C4%2B6%3Db%5C%5C10%3Db%5C%5C)
Therefore, the equation is y=x+10 by substituting the (-6,4) or we can substitute (6,16) too.
![y=mx+b\\y=x+b\\16=6+b\\16-6=b\\10=b\\](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3Dx%2Bb%5C%5C16%3D6%2Bb%5C%5C16-6%3Db%5C%5C10%3Db%5C%5C)
It's the same, you can use any orders given.
Overall, the slope is 1 and the equation is y=x+10
Answer: x<8
interval notation is ( -∞,8)
Step-by-step explanation:
x<8
interval notation is ( -∞,8)
1. divide 8.75 by 3.5 and divide 9.75 by 3.75
2. do 2.5 ×2 plus 1.25
Answer:
It is shifted left 5 units and up 2 units from the parent function.
Step-by-step explanation:
Given
![y = \frac{1}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7Bx%7D)
![y' = \frac{1}{x+5} + 2](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7Bx%2B5%7D%20%2B%202)
Required
Compare both functions
First, translate y, 5 units left.
The rule is:
![(x,y) \to (x + 5,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%20%2B%205%2Cy%29)
So, we have:
![y = \frac{1}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7Bx%7D)
![y_1 = \frac{1}{x + 5}](https://tex.z-dn.net/?f=y_1%20%3D%20%5Cfrac%7B1%7D%7Bx%20%2B%205%7D)
Next, translate y1, 2 units up.
The rule is:
![(x,y) \to (x,y+2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2Cy%2B2%29)
So, we have:
![y' = y_1 + 2](https://tex.z-dn.net/?f=y%27%20%3D%20y_1%20%2B%202)
![y' = \frac{1}{x + 5} + 2](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7Bx%20%2B%205%7D%20%2B%202)
Hence, the transformation is:
5 units left and 2 units up