Get the equation of the line from the table

​Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 -9
2 -13
3 -17
4 -21

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Find the slope of the line by finding the change in y over the change in x, using the first two points.

(1,-9) and (2,-13)  {first two points}

-13 - (-9)
------------- = slope  {change in y over change in x}
2 - 1

slope = -4  {simplified}

Substitute the coordinates of one point, along with the slope, into slope-intercept form,
to find the y-intercept.

(1,-9) , m = -4  {first point and slope}
y = mx + b  {slope-intercept form}
-9 = -4(1) + b  {substituted}
-9 = -4 + b  {multiplied}
b = -5  {added 4 to each side}

slope = -4 and y-intercept = -5

Substitute slope and y-intercept into slope-intercept form to get the equation of the linear function.

y = mx + b  {slope-intercept form}
y = -4x - 5  {substituted}

f(x) = -4x - 5  {wrote in function notation}

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