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Mathematics

Find the equation of the straight line containing the point (3, 2) and making positive equal intercepts on axes.

Straight Line Eq

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Answer

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

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

∴ x = y

Slope of the line=y2−y1x2−x1=0−yx−0=−yx=−xx=−1.\text{Slope of the line} = \dfrac{y2 - 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
⇒ x + y - 5 = 0.

Hence, the equation of the line is x + y - 5 = 0.

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