Explanation:
Hello! remember you have to write complete questions in order to get good and exact answers. Here I'll explain this in a general way assuming the following table:
[tex]\begin{array}{cc}x & y\\0 & 0\\1 & 2\\2 & 4\\3 & 6\\4 & 8\\5 & 10\end{array}[/tex]
As you can see, x increases in steps of 1 units. So let's check the difference in y:
[tex]\bullet \ \text{From x=0 to x=1} \\ \\ \Delta y=2-0=2 \\ \\ \\ \bullet \ \text{From x=1 to x=2} \\ \\ \Delta y=4-2=2 \\ \\ \\ \bullet \ \text{From x=2 to x=3} \\ \\ \Delta y=6-4=2 \\ \\ \\ \bullet \ \text{From x=3 to x=4} \\ \\ \Delta y=8-6=2 \\ \\ \\ \bullet \ \text{From x=4 to x=5} \\ \\ \Delta y=10-8=2[/tex]
So we have a constant difference and we can conclude the table represents a line. Since the line passes through then y is directly proportional to x, so we can write:
[tex]y=kx \\ \\ Where: \\ \\ k \ is \ constant \ of \ proportionality \ or \ the \ slope[/tex]
Then:
[tex]k=\frac{2-0}{1-0}=2[/tex]
Finally, the equation of the line is:
[tex]\boxed{y=2x}[/tex]
