Question

What is the equation of the line that passes through (4, -1) and (-2, 3)?

2 x + 3 y - 5 = 0
-2 x + 3 y - 5 = 0
2 x - 3 y - 5 = 0

Answer 1

2x + 3y - 5 = 0

Explanation:

(4 , -1) & (-2,3)

`Slope =(y_(2)-y_(1))/(x_(2)-x_1)}\\\\=(3-[-1])/(-2-4)\\\\=(3+1)/(-6)\\\\=(4)/(-6)\\\\=(-2)/(3)`

m = -2/3; (4 , -1)

y - y1 = m(x - x1)

`y - [-1]= (-2)/(3)(x-4)\\\\y + 1 =(-2)/(3)x -4*(-2)/(3)\\\\y + 1 =(-2)/(3)x+(8)/(3)`

Multiply the equation by 3

3y + 3 = -2x + 8

3y = -2x + 8 - 3

3y = -2x + 5

2x + 3y - 5 = 0