In order to find which equation matches the graph, we need to use the points in the graph to find the corresponding equation.
We can use the linear equation y = ax + b to model the graph, and then, using the points, we can find the value of 'a' in our equation.
In the graph, we can see the points (1, 4), and (3, 12), so using the values x = 1 and y = 4 in the equation, we have:
[tex]\begin{gathered} y=ax+b \\ 4=a\cdot1+b \\ a+b=4 \end{gathered}[/tex]
Now, using the values x = 3 and y = 12, we have:
[tex]\begin{gathered} y=ax+b \\ 12=a\cdot3+b \\ 3a+b=12 \end{gathered}[/tex]
Subtracting the second equation we got by the first one, we have:
[tex]\begin{gathered} 3a+b-(a+b)=12-4 \\ 3a+b-a-b=8 \\ 2a=8 \\ a=4 \\ \\ a+b=4\to4+b=4\to b=0 \end{gathered}[/tex]
So our equation is:
[tex]y=4x[/tex]
Therefore the answer is D.
