**Question:**

Find the equation of the line passing through the point P(4, - 5) and parallel to the line joining the points A(3, 7) and B( - 2, 4).

**Solution:**

As two points passing through a line parallel to the line are given, we will calculate slope using two points(slope of parallel lines is equal).

$\mathrm{m}=\frac{\mathrm{y}_{2-\mathrm{y}_{1}}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{4-7}{-2-3}=\frac{-3}{-5}$

$\mathrm{m}=\frac{3}{5}$

Now using the slope - intercept form, we will find intercept for a line passing through (4, - 5)

$y=m x+c$ .....................(1)

$-5=\frac{3}{5}(4)+c \Rightarrow-5-\frac{12}{5}=c$

$c=\frac{-25-12}{5} \Rightarrow c=-\frac{37}{5}$

Putting value in equation (1)

$y=\frac{3}{5}(x)+\left(\frac{-37}{5}\right) \Rightarrow 3 x-5 y-37=0$

So, the required equation of line is $3 \mathrm{x}-5 \mathrm{y}-37=0$