Question

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.

[Hint. Let each intercept be a units.
Then, this line passes through A(a, 0) and B(0, a).
Equation of AB is `(y - 0)/(x - a) = (a - 0)/(0 - a) ⇒ y = -x + a.`
Since, it passes through (3, 2), we get a = 5.
∴ Required equation is x + y = 5.]

Answer 1

Let the equal positive intercept on each axis be $$a$$, where $$a > 0$$. The line passes through $$(a, 0)$$ and $$(0, a)$$.

Slope of the line: $$m = \frac{a - 0}{0 - a}$$

$$= \frac{a}{-a}$$

$$= -1$$

Since the $$y$$-intercept is $$a$$, the equation of the line is:

$$y = -x + a$$

$$\implies x + y = a$$

Since the line passes through $$(3, 2)$$, substitute $$x = 3$$ and $$y = 2$$:

$$3 + 2 = a$$

$$\implies a = 5$$

Therefore, the length of each intercept is $$5$$ units and the equation of the line is $$x + y = 5$$ or $$x + y - 5 = 0$$.