Find the equation of the linear function

Find the equation of the linear function represented by the table below in slope-intercept form.
x   y
1   -1
2   0
3   1
4   2

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To get the equation of a line, you need a point and the slope. To find the slope, choose any two points, then find the change in y over the change in x.

(1,-1) and (2,0) are two points on the line.

0 - (-1)
-------   = slope  {change in y-coordinates over change in x-coordinates}
2 - 1

1
-- = slope {subtracted in numerator and denominator}
1

slope = 1  {reduced}

Substitute a point and the slope into slope-intercept form.

slope is 1 and a point is (2,0)

y = mx + b   {slope-intercept form}
0 = 1(2) + b   {substituted 2 for x, 0 for y, and 1 for m into slope-intercept form}
0 = 2 + b   {multiplied 1 by 2}
b = -2   {subtracted 2 from each side}
the y-intercept is -2

Substitute the slope and y-intercept back into slope-intercept form.

y = mx + b   {slope-intercept form}
y = 1x - 2   {substituted 1 for m (the slope) and -2 for b (the y-intercept}
y = x - 2 is the equation of the line.

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