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, -3)
(2 -1)
(3, 1)
(4, 3)

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Get the slope of the line, by taking two points and finding the change in y over the change in x.

change in y
——————— = slope
change in x

(1,-3) and (2,-1) {took the first and second points, it does not matter which two points you choose}

-1 - (-3)
————— = slope {change in y coordinates over change in x coordinates}
2 - 1

2
— = slope {subtracted in numerator and denominator}
1

slope = 2

Take the slope, along with one of the points, and substitute into slope-intercept form,
to find the y-intercept.

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

(1,-3) and slope = 2 {it does not matter which point you choose}
-3 = 2(1) + b {substituted -3 for y, 2 for m, and 1 for x}
-3 = 2 = b {multiplied 2 by 1}
b = -5 {subtracted 2 from each side}
y-intercept is -5
​
Substitute the slope and y-intercept back into slope-intercept form.

slope = 2 and y-intercept = -5

y = mx + b {slope-intercept form}
y = 2x - 5 is the equation of the linear function

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