Mathematics

Prove that the line through (0, 0) and (2, 3) is parallel to the line through (2, -2) and (6, 4).

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The slope of the line passing through two points (x₁, y₁) and (x₂, y₂) is given by

Slope = $\dfrac{y$ .

So, slope (m₁) of (0, 0) and (2, 3) is,

$= \dfrac{3 - 0}{2 - 0} \\[1em] = \dfrac{3}{2}.$

So, slope (m₂) of (2, -2) and (6, 4) is,

$= \dfrac{4 - (-2)}{6 - 2} \\[1em] = \dfrac{6}{4} \\[1em] = \dfrac{3}{2}.$

Since, m₁ = $\dfrac{3}{2}$ = m₂.

Hence, the lines are parallel to each other.

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