Question

Find the gradient and the equation of the line passing through the points:

$$\mathrm{A}(4, -2)$$ and $$\mathrm{B}(2, -3)$$

Answer 1

The gradient of a line passing through $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ and the equation of the line is $$y - y_1 = m(x - x_1)$$

For $$\mathrm{A}(4, -2)$$ and $$\mathrm{B}(2, -3)$$:

$$m = \frac{-3 - (-2)}{2 - 4}$$

$$= \frac{-3 + 2}{-2}$$

$$= \frac{-1}{-2}$$

$$= \frac{1}{2}$$

Equation of the line:

$$y - (-2) = \frac{1}{2}(x - 4)$$ 

$$y + 2 = \frac{1}{2}(x - 4)$$ 

$$2(y + 2) = x - 4$$ 

$$2y + 4 = x - 4$$ 

$$x - 2y - 8 = 0$$