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 -10
3 -14
4 -18

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To get the equation, first find the slope of the line by using any two points.  Subtract the y-coordinates over the subtraction of the x-coordinates.  {change in y over change in x}

(1,-6) and (2,-10)  {the first two points, but any two points will work}

-10 - (-6)
---------- = slope  {change in y over change in x}
2 - 1

-4
--- = slope {subtracted in numerator and denominator}
1

slope = -4

Substitute the slope, along with one of the points, into slope-intercept form, y = mx + b, to find the y-intercept.

(1,-6) and m = -4 {the first point and the slope}
y = mx + b  {slope-intercept form}
-6 = -4(1) + b   {substituted 1 in for x, -6 in for y, and -4 in for m}
-6 = -4 + b  {multiplied}
b = -2   {added 4 to each side}
y-intercept = -2

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

y = mx + b  {slope-intercept form}
y = -4x - 2

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