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Mathematics

Find the equation of a line passing through the point (2, 3) and having the x-intercept of 4 units.

Straight Line Eq

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Answer

Let the line intersect x-axis at point A.

So, A = (4, 0).

Let B = (2, 3).

By formula,

Slope = y2−y1x2−x1\dfrac{y2 - y1}{x2 - x1}

Slope of AB = 3−02−4=−32\dfrac{3 - 0}{2 - 4} = -\dfrac{3}{2}.

By point-slope form,

⇒ y - y1 = m(x - x1)

⇒ y - 0 = −32-\dfrac{3}{2}(x - 4)

⇒ 2y = -3(x - 4)

⇒ 2y = -3x + 12

⇒ 3x + 2y = 12.

Hence, the equation of required line is 3x + 2y = 12.

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