Question

If a line passing through the points (4, - p) and (-2, 6)
parallel to the line having an equation 2y + 3x = -3, find
the value of p.
​

Answer 1

Let X be the line passing through (4, -p) and (-2, 6)

Slope of X

$=\frac{6-(-p)}{-2-4}=-\frac{p+6}{6}$

Let Y be the line represented by the equation 2y + 3x = -3

$2x+3y=-3\\\implies 3y = -2x -3\\\implies y = (-\frac{2}{3})x+(-1)$

Which is of the form $y=mx+c$, where m = slope of Y = -2/3 and c = -1

Since X || Y,

Slope of X = Slope of Y

$\implies -\frac{p+6}{6} =-\frac{2}{3} \\\implies \frac{p+6}{6} = \frac{2}{3}\\\implies 3p+18=12\\\implies 3p=-6\\\therefore p=-2$