Answer:
C
Step-by-step explanation:
We know that line CD passes through the two points (0, 2) and (4, 6).
First and foremost, let’s find the slope of the line. We can use the slope formula:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let’s let (0, 2) be (x₁, y₁) and (4, 6) be (x₂, y₂). Substitute appropriately:
![\displaystyle m=\frac{6-2}{4-0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B6-2%7D%7B4-0%7D)
Evaluate:
![\displaystyle m=\frac{4}{4}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B4%7D%7B4%7D%3D1)
Hence, our slope is 1.
Now, we can use the slope-intercept form:
![\displaystyle y=mx+b](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dmx%2Bb)
Where m is our slope and b is our y-intercept.
Notice from our given points that we are given (0, 2).
So, our y-intercept is 2.
Therefore, we will substitute 1 for m and 2 for b. This yields:
![\displaystyle y=(1)x+(2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%281%29x%2B%282%29)
Simplify:
![\displaystyle y=x+2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dx%2B2)
Hence, our answer is C.