Not necessarily.
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You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
table of values,x and y-intercept and slope and y-intercept
Yes, y = 3+x is linear.
Yes, y=x-4 is linear, since the highest power on x is 1 (y = x1-4)
Yes, y=-2+x is a linear function.