Question

[21] A straight line passes through the
point(3, 2). Find the equation-of-the-
straight line:​

Answer 1

Answer :

The required equation of line is  :

2x+3y = 12

Step-by-step explanation :

Given that :

This line is bisected by the point (3,2).

To Find :

The equation of the line.

Solution :

Let the line intersect x-axis at (x,0) & y-axis at (0,y)

$\sf \implies (3,2) = \dfrac{(x+0)}{2},\dfrac{(0+y)}{2}\\ \\\implies 3 = \dfrca{x}{2}\\ \\\implies x = 6\\ \\\implies 2 = \dfrac{y}{2}\\ \\\implies y = 4\\ \\\\\textbf{It implies that the line intersects x-axis at (6,0) and y-axis at (0,4)}$

$\textbf{\underline{\underline{The\; equation\; of line\; of\; two\; point\; form\; is\; given\; by :}}}\\ \\\sf \implies (y-y_1) =\dfrac{(y_2-y_1)}{(x_2-x_1)} \times (x-x_1)\\ \\\implies (y-0) =\dfrac{(4-0)}{(0-6)}\\ \\ \implies (x-6)\\ \\\implies y = \dfrac{(4}{-6)} \times (x-6)\\ \\\implies y = \dfrac{2}{-3} \times x - \dfrac{2}{-3} \times(-6)\\ \\\implies y = \dfrca{2x}{-3} - (4)\\ \\\implies y = \dfrac{(2x-12)}{-3}\\ \\\implies -3y = 2x-12\\ \\\implies 2x+3y = 1$

$\bigstar\; \textbf{{\underline}{\underline{Hence the required equation of line is\;2x+3y = 12}}}}$