Question Video: Finding the Equation of a Straight Line in Parametric Form Mathematics

Straight line 𝐿 passes through the point 𝑁 (3, 4) and has a direction vector 𝐮 = 〈2, −5〉. Then, the parametric equations of line 𝐿 are _.

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Video Transcript

Straight line 𝐿 passes through the point 𝑁 with coordinates three, four and has a direction vector 𝐮 equal to two, negative five. Then the parametric equations of line 𝐿 are what.

We begin by recalling that the parametric form of the equation of a line passing through the point 𝑥 sub zero, 𝑦 sub zero and parallel to the direction vector 𝑎, 𝑏 is 𝑥 is equal to 𝑥 sub zero plus 𝑎𝑡 and 𝑦 is equal to 𝑦 sub zero plus 𝑏𝑡. We are told in the question that the straight line 𝐿 passes through the point with coordinates three, four. This means that our value of 𝑥 sub zero is three and 𝑦 sub zero is equal to four. We are also given a direction vector 𝐮 such that 𝑎 is equal to two and 𝑏 is negative five.

Substituting in our values of 𝑥 sub zero and 𝑎, we get 𝑥 is equal to three plus two 𝑡. And substituting the values of 𝑦 sub zero and 𝑏, we get 𝑦 is equal to four minus five 𝑡. It is important to note that we could replace the letter 𝑡 with any other letter as the parameter. For example, 𝑥 is equal to three plus two 𝑘 and 𝑦 is equal to four minus five 𝑘 is also a valid solution. We can therefore conclude that these are the parametric equations of line 𝐿.

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