Find the equation represented by the table

Find the equation of the linear function represented by the table below in slope-intercept form.
x   y
1   6
2   8
3   10
4   12

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Find the slope of the line by choosing any two points, and finding the change in y over the change in x.

(1,6) and (2,8) are two points on the line

8 - 6
----- = slope of the line  {change in y over the change in x}
2 - 1

slope = 2  {subtracted in numerator and denominator}

Substitute the slope and one of the points into slope-intercept form to find the y-intercept.

slope = 2 and (1,6) is a point
y = mx + b   {slope-intercept form}
6 = 2(1) + b  {substitute x and y-coordinates, along with the slope, into slope-intercept form}
6 = 2 + b  {muiltiplied 2 by 1}
b = 4   {subtracted 2 from each side}
 
y-intercept is 4

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

y = mx + b  {slope-intercept form}
y = 2x + 4 is the equation of the line  {subsituted}

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