Find the equation of the line passing through the point (3, 2) and making positive equal intercepts on axes. Find the length of each intercept.

Let the line containing the point (3, 2) passes through x-axis at A(x, 0) and y-axis at B(0, y).

Given, the intercepts made on both the axes are equal.

∴ x = y

Slope of the line

$m = \dfrac{y$2 - y1}{x2 - x1} \\[1em] = \dfrac{0 - y}{x - 0} \\[1em] = \dfrac{-y}{x} \\[1em] = \dfrac{-x}{x} \\[1em] = -1.

Hence, the equation of the line will be

⇒ y - y₁ = m(x - x₁)

⇒ y - 2 = -1(x - 3)

⇒ y - 2 = -x + 3

⇒ y + x - 2 - 3 = 0

⇒ y = -x + 5.

Comparing above equation with y = mx + c, we get :

c = 5.

Thus, y-intercept = 5.

∴ x-intercept = 5.

Hence, equation of line is x + y = 5 and length of x and y intercept is 5 units.