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A line in parametric form

A straight line can be written as a starting point plus the parameter times a direction vector. Each value of $t$ gives one point on the line. If you want to know where the line crosses an axis, you set that coordinate equal to zero and solve for $t$. Then you insert that value into the other coordinate. Two different choices of parameter can describe the same line.

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Example

The line through $(1, 2)$ with direction $[3, -1]$ is $x = 1 + 3t$ and $y = 2 - t$. For $t = 2$ the point has $x = 7$ and $y = 0$. Crossing the $y$-axis: $t = -0.3333$.

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Part of Mathematics R1: Parametric curves.