Question

A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = (x – 2). Which equations also represent this line? Check all that apply. 1. y = -5/3 x – 2
2. y = -5/3 x + 10/3
3. 3y = –5x + 10
4. 3x + 15y = 30
5. 5x + 3y = 10

Answer 1

The answers are b. c. and e.

Answer 2

Recall that the equation of a line passing through two points (x1, y1 and (x2, y2) is given by the formula (y - y1) / (x - x1) = (y2 - y1) / (x2 - x1). Given that the line passes through the points (-4, 10) and (-1, 5), the equation of the line is given by (y - 10) / (x - (-4)) = (5 - 10) / (-1 - (-4)) = -5 / 3 3(y - 10) = -5(x + 4) 3y - 30 = -5x - 20 3y = -5x + 10 5x + 3y = 10 y = -5/3 x + 10/3