The table gives the distance traveled over a certain time. what is the value of a that will result in a constant rate of change?

Maybe one of the easier ways to work this is to write the equation of the line through the points you know, then use that to find the point you don't know. The 2-point formula for a line is ...

... y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in (x1, y1) = (3, 213) and (x2, y2) = (8, 568), you get ...

... y = (568 -213)/(8 -3)·(x -3) +213

... y = 71(x -3) +213 . . . . . . simplified a bit

Now, for x=5, the value of a is ...

... a = 71(5 -3) +213 = 142 +213 = 355

The value of a that results in a constant rate of change is 355.

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The equation can actually be simplified further to ...

... y = 71x