Find an arc length parameterization of the line $y=6x+7$. Confused on how to start with x's and y's.
2026-04-01 23:25:57.1775085957
Finding Arc Length Parametrization
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Hint: Everytime you have $y = y(x)$, you can write your curve as $\gamma(x) = (x,y(x))$, for example. So you can write $\gamma(x) = (x,6x+7)$, which is exactly the same as $\gamma(t) = (t,6t+7)$. So, we have: $$s(t) = \int_0^t \|\gamma'(\tau)\|\,{\rm d}\tau,$$ which is easy to compute. So you can find $t$ in terms of $s$, and substitute in the expression for $\gamma(t)$. Now it's on you.