Question

Fine the equation, in standard form, of the line passing through the points (3,-4) and (5,1)

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have the points (3, -4) and (5, 1). Substitute:

`m=(1-(-4))/(5-3)=(5)/(2)\\\\y-(-4)=(5)/(2)(x-3)`

The standard form:
`Ax+By=C`

`y+4=(5)/(2)(x-3)` multiply both sides by 2

`2y+8=5(x+3)` use distributive property

`2y+8=5x+15` subtract 2y from both sides

`8=5x-2y+15` subtract 15 from both sides

`-7=5x-2y`

Answer: 5x - 2y = -7