# Find the equation of the line through points (2, 2) and (4, 10) and what is the equation of the line through points (2, 8) and (3, -2)?

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The equation of the line through the points (2, 2) and (4, 10) is:

`(y - 2)/(x - 2) = (10 - 2)/(4 - 2)`

=> `(y - 2)/(x - 2) = 8/2`

=> `(y - 2)/(x - 2) = 4`

=> y - 2 = 4x - 8

=> 4x - y - 6 = 0

The equation of the line through (2, 8) and (3, -2) is:

`(y + 2)/(x - 3) = (8 + 2)/(2 - 3)`

=> `(y + 2)/(x - 3) = -10`

=> y + 2 = -10x + 30

=> 10x + y - 28 = 0

The general equation of the line through points (X1, Y1) and (X2, Y2) is given by:

`(y - Y2)/(x - X2) = (Y1 - Y2)/(X1 - X2)`

For the points (2, 2) and (4, 10) substituting the values in the given formula gives:

`(y - 2)/(x - 2) = (10-8)/(4 - 2)`

`(y - 2)/(x - 2) = 2/2`

`(y - 2)/(x - 2) = 1`

For the points (2, 8) and (3, -2) substituting the values in the given formula gives:

`(y - 8)/(x - 2) = (-2 - 8)/(3 - 2)`

`(y - 8)/(x - 2) = -10`