Answer: The correct option is (C) [tex]y=x+2.[/tex]
Step-by-step explanation: Given that the line CD passes through the points (0, 2) and (4, 6).
We are to select the equation that represents line CD.
The slope of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of line CD is given by
[tex]m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1.[/tex]
Since the line CD passes through the point (0, 2), so its equation will be
[tex]y-2=m(x-0)\\\\\Rightarrow y-2=1\times x\\\\\Rightarrow y-2=x\\\\\Rightarrow y=x+2.[/tex]
Thus, the required equation of line CD is [tex]y=x+2.[/tex]
Option (C) is CORRECT.
