The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (-8, -20) and (5, 2). Substitute:
![m=\dfrac{2-(-20)}{5-(-8)}=\dfrac{22}{13}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B2-%28-20%29%7D%7B5-%28-8%29%7D%3D%5Cdfrac%7B22%7D%7B13%7D)
Answer: The slope is ![\dfrac{22}{13}](https://tex.z-dn.net/?f=%5Cdfrac%7B22%7D%7B13%7D)
Answer:
-56
Step-by-step explanation:
f(x) = 7x + 7
x = -9
We meed to plug in x = -9 into the first equation:
f(-9) = 7(-9) + 7
We can open up the parentheses:
f(-9) = -63 + 7
And then simplify:
f(-9) = -56
Answer:
![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
Step-by-step explanation:
Method 1:
Arithmetic sequence is in the form
![a_{n} =a_{1} +(n-1)d\\](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3Da_%7B1%7D%20%2B%28n-1%29d%5C%5C)
d is the common difference, can be found by:
![d=a_{n}-a_{n-1}=-3](https://tex.z-dn.net/?f=d%3Da_%7Bn%7D-a_%7Bn-1%7D%3D-3)
Subtituting the
and ![d](https://tex.z-dn.net/?f=d)
You get:
![a_{n}=42+(-3)(n-1)=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D42%2B%28-3%29%28n-1%29%3D45-3n)
Method 2 (Mathematical induction):
Assume it is in form ![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
Base step: ![a_{1} =45-3(1)=42](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D45-3%281%29%3D42)
Inducive hypophesis: ![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
GIven: ![a_{n+1} =a_{n}-3](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3Da_%7Bn%7D-3)
![a_{n+1}=45-3n-3=45-3(n+1)](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3D45-3n-3%3D45-3%28n%2B1%29)
Proved by mathematical induction
![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
Answer:
slope: -3/5
y-intercept (0,3)
x - y
0 3
5 0
Step-by-step explanation:
I just did it