Question

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

$$\mathrm{A}(-2, 1)$$ and $$\mathrm{B}(3, -4)$$

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 $$\mathrm{A}(-2, 1)$$ and $$\mathrm{B}(3, -4)$$:

$$m = \frac{-4 - 1}{3 - (-2)}$$

$$= \frac{-5}{5}$$

$$= -1$$

Equation of the line:

$$y - 1 = -1(x - (-2))$$

$$y - 1 = -(x + 2)$$

$$y - 1 = -x - 2$$

$$x + y + 1 = 0$$