Question

Solve m=
`\frac{y_(2)- {y_(1)} }{x_2-x_(1) }` for
`y_(2)`

Answer 1

`y_2 = (x_2 - x_1) +y_1`.

Implied:
`x_2\\e x_1`.

Explanation:

Get rid of the denominator by multiplying both sides of this equation with
`(x_2 - x_1)`:

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

Isolate
`y_2` by moving
`(-y_1)` to the left-hand side of the equation. That is: add
`y_1` to both sides of this equation.

`m(x_2 - x_1) + y_1 = y_2`.

By the symmetric property of equalities,

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