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Problem: line through (5,5) and parallel to line passing (1,-2) and (-5,2) [ Calculator, Method and examples ]

Your problem `->` line through (5,5) and parallel to line passing (1,-2) and (-5,2)

When two lines are parallel, their slopes are equal.
We shall first find the slope of `(1,-2)` and `(-5,2)`

Points are `B(1,-2), C(-5,2)`

`:. x_1=1, y_1=-2, x_2=-5, y_2=2`

Slope = `m = (y_2-y_1)/(x_2-x_1)`

`:. m = (2+2)/(-5-1)`

`:. m = (4)/(-6)`

`:. m = -2/3`

`:.` Slope`=-2/3` and hence slope of the line parallel to this line is also `-2/3`

The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`

Putting `(5,5)` for `(x_1,y_1)` and `m=-2/3,` we get

`:. y-5=-2/3(x-5)`

`:. 3(y-5)=-2(x-5)`

`:. 3y -15=-2x +10`

`:. 2x+3y-25=0`

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