Question

Find the equation of a line passing through the point $$\mathrm{P}(-2, 1)$$ and parallel to the line joining the points $$\mathrm{A}(4, -3)$$ and $$\mathrm{B}(-1, 5)$$.

Answer 1

Slope of line $$\mathrm{AB}$$ joining $$\mathrm{A}(4, -3)$$ and $$\mathrm{B}(-1, 5)$$: 

$$m = \frac{5 - (-3)}{-1 - 4}$$

$$= \frac{8}{-5}$$

$$= -\frac{8}{5}$$

Since the required line is parallel to $$\mathrm{AB}$$, its slope is also $$m = -\frac{8}{5}$$. 

The line passes through $$\mathrm{P}(-2, 1)$$: 

$$y - 1 = -\frac{8}{5}(x - (-2))$$ 

$$5(y - 1) = -8(x + 2)$$ 

$$5y - 5 = -8x - 16$$ 

$$8x + 5y + 11 = 0$$