Answer:
[tex]y_2 = (x_2 - x_1) +y_1[/tex].
Implied: [tex]x_2\ne x_1[/tex].
Step-by-step explanation:
Get rid of the denominator by multiplying both sides of this equation with [tex](x_2 - x_1)[/tex]:
[tex]m(x_2 - x_1) = y_2 - y_1[/tex].
Isolate [tex]y_2[/tex] by moving [tex](-y_1)[/tex] to the left-hand side of the equation. That is: add [tex]y_1[/tex] to both sides of this equation.
[tex]m(x_2 - x_1) + y_1 = y_2[/tex].
By the symmetric property of equalities,
[tex]y_2 = m(x_2 - x_1) + y_1[/tex]
