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  6
2  9
3  12
4  15

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Find the slope of the line, by choosing two points and subtracting the y-coordinates over the x-coordinates.

y2 - y1
------- = slope
x2 - x1

9 - 6
------  = slope  {change in y over change in x}
2 - 1

slope = 3

Choose one of the points and substitute, with the slope, into slope-intercept form.

y = mx + b  {slope-intercept form}
m is the slope
b is the y-intercept

point is (1,6) and slope is 3
y = mx + b
6 = 3(1) + b  {substituted 1 in for x, 6 in for y, and 3 in for m, into slope-intercept form}
6 = 3 + b  {multiplied 3 by 1}
b = 3  {subtracted 3 from each side}
y-intercept = 3

f(x) = 3x + 3 is the linear function  {substituted slope and y-intercept back into slope-intercept form}

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