The equation of blue line is y= 1/2x+2.
<h3>What is equation of line?</h3>
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.
As from the graph we can see that the y - intercept is 2.
Also the function crosses y - axis at 2.
So, slope of the function is 1/2.
Now using
slope= rise/ run
1/2= y/x
y= 1/2x
Now, slope intercept form: y = mx + b
y= 1/2x+2
Learn more about equation of line here:
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![\huge \boxed{\mathbb{QUESTION} \downarrow}](https://tex.z-dn.net/?f=%20%5Chuge%20%5Cboxed%7B%5Cmathbb%7BQUESTION%7D%20%5Cdownarrow%7D)
- Solve ⇨ (x + 1)(x + 2) • (x + 2)(x - 2)
![\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7B%5Cmathfrak%7BAnswer%20%5C%3A%20with%20%5C%3A%20Explanation%7D%20%5Cdownarrow%7D)
![( x + 1 ) ( x + 2 ) \cdot ( x + 2 ) ( x - 2 )](https://tex.z-dn.net/?f=%28%20x%20%2B%201%20%29%20%28%20x%20%2B%202%20%29%20%5Ccdot%20%28%20x%20%2B%202%20%29%20%28%20x%20-%202%20%29)
Multiply x+2 and x+2 to get
.
![\left(x+1\right)\left(x+2\right)^{2}\left(x-2\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2B1%5Cright%29%5Cleft%28x%2B2%5Cright%29%5E%7B2%7D%5Cleft%28x-2%5Cright%29%20)
Use binomial theorem
to expand
.
![\left(x+1\right)\left(x^{2}+4x+4\right)\left(x-2\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2B1%5Cright%29%5Cleft%28x%5E%7B2%7D%2B4x%2B4%5Cright%29%5Cleft%28x-2%5Cright%29%20)
Apply the distributive property by multiplying each term of x+1 by each term of x²+4x+4.
![\left(x^{3}+4x^{2}+4x+x^{2}+4x+4\right)\left(x-2\right)](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B3%7D%2B4x%5E%7B2%7D%2B4x%2Bx%5E%7B2%7D%2B4x%2B4%5Cright%29%5Cleft%28x-2%5Cright%29%20)
Combine 4x² and x² to get 5x².
![\left(x^{3}+5x^{2}+4x+4x+4\right)\left(x-2\right)](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B3%7D%2B5x%5E%7B2%7D%2B4x%2B4x%2B4%5Cright%29%5Cleft%28x-2%5Cright%29%20)
Combine 4x and 4x to get 8x.
![\left(x^{3}+5x^{2}+8x+4\right)\left(x-2\right)](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B3%7D%2B5x%5E%7B2%7D%2B8x%2B4%5Cright%29%5Cleft%28x-2%5Cright%29%20)
Apply the distributive property by multiplying each term of x³+5x²+8x+4 by each term of x-2.
![x^{4}-2x^{3}+5x^{3}-10x^{2}+8x^{2}-16x+4x-8](https://tex.z-dn.net/?f=x%5E%7B4%7D-2x%5E%7B3%7D%2B5x%5E%7B3%7D-10x%5E%7B2%7D%2B8x%5E%7B2%7D-16x%2B4x-8%20)
Combine -2x³ and 5x³ to get 3x³.
![x^{4}+3x^{3}-10x^{2}+8x^{2}-16x+4x-8](https://tex.z-dn.net/?f=x%5E%7B4%7D%2B3x%5E%7B3%7D-10x%5E%7B2%7D%2B8x%5E%7B2%7D-16x%2B4x-8%20)
Combine -10x² and 8x² to get -2x².
![x^{4}+3x^{3}-2x^{2}-16x+4x-8](https://tex.z-dn.net/?f=x%5E%7B4%7D%2B3x%5E%7B3%7D-2x%5E%7B2%7D-16x%2B4x-8%20)
Combine -16x and 4x to get -12x.
![\large \boxed{ \boxed{\bf \: x^{4}+3x^{3}-2x^{2}-12x-8 }}](https://tex.z-dn.net/?f=%20%5Clarge%20%20%5Cboxed%7B%20%5Cboxed%7B%5Cbf%20%5C%3A%20x%5E%7B4%7D%2B3x%5E%7B3%7D-2x%5E%7B2%7D-12x-8%20%7D%7D)
Answer:
-2/3
Step-by-step explanation:
This value is very different from the other values