Question

find tge equation of a line passing through the point P(4,-5) and parallel to the line passing through the points A(3,7) and B(-2,4)​

Answer 1

The considered line is parallel to AB

hence, slope of AB = slope of the line

slope of AB, m

$m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } \\ m = \frac{4 - 7}{ - 2 - 3} = \frac{ - 3}{ - 5} \\ m = \frac{ 3}{ 5}$

Let P(4, -5) = (p, q)

Equation of the line passing through P(4, -5), using the slope-point formula–

$y - q = m(x - p) \\ y - ( - 5) = \frac{3}{5} (x - 4) \\ 5y + 25 = 3x - 12 \\ 3x - 5y - 37 = 0$

Hence, equation of the desired line is

3x - 5y - 37 = 0