converting from cartesian to parametric form (1 Viewer)

Run hard@thehsc

Active Member
Can someone help me with regard to this?
Like how would you convert a line y = 8x + 5 to a parametric form? thanks!!!

Masaken

Member
let x = t
then just replace x in the Cartesian with t

x = t, y = 8t + 5

If I recall correctly this question has 'infinite' solutions as you can replace t with any other letter to be a parameter

Drongoski

Well-Known Member
y = 8x + 5

So, take any point on the line like (1, 13) or (0, 5)

Gradient m = 8 means x : y = 1 : 8 so a direction vector is $\bg_white \binom 1 8$

So a vector equation of y = 8x + 5 is: $\bg_white \binom x y = \binom 1 {13} + \lambda \binom 1 8$

Correction: I thought it was for a vector equation.

For my example, a parametric eqn would simply be: $\bg_white x = 1 + \lambda and y = 13 + 8\lambda$

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