Question

Write the equation of the line passing through A(–3, 4) and B(4, 5) in the form of ax + by + c = 0

Answer 1

`A(-3,4) B(4,5)

Let `A(-3,4) ≡ (x_1,y_1); B(4,5) ≡ (x_2, y_2)`

Now, `(x-x_1)/(x_1 - x_2) = (y - y_1)/(y_1 - y_2)`

`:. (x-(-3))/(-3-4) = (y - 4)/(4 - 5)`     ∴ `(x+3)/(-7) = (y -4)/(-1)`

∴ -1(x + 3) = -7(y - 4)

∴ -x - 3 = -7y + 28

∴ -x + 7y - 3 - 28 = 0           ∴ x - 7y + 31 = 0

The equation of the line AB is x - 7y + 31 = 0