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:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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:
[tex]\displaystyle m=\frac{6-2}{4-0}[/tex]
Evaluate:
[tex]\displaystyle m=\frac{4}{4}=1[/tex]
Hence, our slope is 1.
Now, we can use the slope-intercept form:
[tex]\displaystyle y=mx+b[/tex]
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:
[tex]\displaystyle y=(1)x+(2)[/tex]
Simplify:
[tex]\displaystyle y=x+2[/tex]
Hence, our answer is C.
