Question

If a line is passing through the points (-3,4) and (2,5) is parallel to
the line kx + 3y = 8, then value of k is​

Answer 1

Equation of line passing through two points (x1,y1) and (x2,y2) :-

$\sf y-y_1=x-x_1 \dfrac{(y_2-y_1) }{(x_2-x_1)}$

Now here equation of line is passing through :-

(-3,4) and (2,5)

There, equation of line :-

$\sf \implies \: y-4=(x-( - 3)) \dfrac{(5 - 4) }{(2 - ( - 3))}$

$\sf \implies \: y-4=(x + 3) \dfrac{1 }{5}$

$\sf \implies \: 5(y-4)=(x + 3)$

$\sf \implies \: 5y-20=x + 3$

$\sf \implies \: - x + 5y-23=0$

Now slope of line when equation of line is given :-

$\bf \: slope= - \dfrac{ coefficient \: of \: x}{coefficient \: of \: y}$

Now , we know that slope of parallel lines are equal.

Therefore , according to the question :-

$\implies\sf \: - \dfrac{ k}{3} = - \dfrac{ - 1}{5}$

$\implies\sf \: { k} = \dfrac{ -3}{5}$

Answer :

value of k = -3/5