Question

Lindsay used two points, (x 1, y 1) and (x 2, y 2), to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. Given this information, which expression must represent the value of b?
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)

Answer 1

Use y = mx + b with (x1,y1): b = y1 - m x1. With m = (y2 − y1)/(x2 − x1), b = y1 − ((y2 − y1)/(x2 − x1))·x1. So the first expression is correct.