Question

Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).

Answer 1

5x - 2y = -4

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

Te formula of a slope:

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

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We have two points: (2, -3) and (4, 2). Substitute:

`m=(2-(-3))/(4-2)=(5)/(2)`

`y-(-3)=(5)/(2)(x-2)\\\\y+3=(5)/(2)(x-2)`

Convert it to the standard form
`Ax+By=C`:

`y+3=(5)/(2)(x-2)` multiply both sides by 2

`2y+6=5(x+2)` use the coordinates of the point

`2y+6=5x+10` subtract 6 from both sides

`2y=5x+4` subtract 5x from both sides

`-5x+2y=4` change the signs

`5x-2y=-4`