A change in x of 2 from one row to the next gives a change in y of 6. For example, changing x from -3 to -1 gives a change in y from -8 to -2. Then the slope is
... slope = ∆y/∆x = 6/2 = 3 . . . . . the coefficient of x
Now, you can pick any row of the table to determine what the intercept value must be. For example, choosing x = 1, we have
... 4 = 3×1 + intercept
... 1 = intercept . . . . . . . subtract 3 from both sides of the equation
Now, you know your equation is
... y = 3x + 1
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Since this is a linear equation, the y-intercept at x=0 will be halfway betweeen the value of y at x=-1 and the value of y at x=1. That is (-2+4)/2 = 1, in agreement with our calculation above.