The equation of the line passes through A(3,5) and B(-6,2)

First, we will find the slope.

==> `m= (5-2)/(3-(-6)) = 3/9= 1/3`

`==> y-y1 = m (x-x1)`

`==> y-5 = (1/3) (x-3)`

`==> y-5 = (1/3)x -1`

`==> y= (1/3)x +4 `

`` Now we will find the equation of the line that passes through B(-6,2) and C(4,-4)

`==> m= (-4-2)/(4+6) = -6/10 = -3/5`

`==> y-y1 = m(x-x1)`

`==> y +4 = (-3/5) (x-4)`

`==> y= (-3/5)x + 12/5 -4`

`==> y= (-3/5)x - 8/5`

`` Now we will find the equation of the line that passes through A(3,5) and C(4,-4)

`==> m= (-4-5)/(4-3)= -9/1 = -9`

`==> y-y1 = m(x-x1)`

`==> y-5 = -9(x -3)`

`==> y= -9x +27 +5`

`==> y= -9x +32`

``

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