Question

Points \(\mathrm{A}(x, y), \mathrm{B}(3, -2)\) and \(\mathrm{C}(4, -5)\) are collinear. The value of y in terms of x is ______.

Options

• \(3x - 11\)

• \(11 - 3x\)

• \(3x - 7\)

• \(7 - 3x\)

Answer 1

Points \(\mathrm{A}(x, y), \mathrm{B}(3, -2)\) and \(\mathrm{C}(4, -5)\) are collinear. The value of y in terms of x is 3x – 11.

Explanation:

Slope of \(BC = \frac{-5 - (-2)}{4 - 3} = -3\).

Since \(A(x, y)\) lies on this line:

$$y - (-2) = -3(x - 3)$$

$$\Rightarrow y = 7 - 3x$$