### Home > CALC > Chapter 10 > Lesson 10.1.8 > Problem10-81

10-81.

Find the arclength of the curve $y = mx + b$ $(m ≠ 0)$ from $x = k_1$ to $x = k_ 2 (k_l < k_2)$ using the arclength formula. Then verify your result using the Pythagorean theorem. Illustrate your work with a diagram.

$=\left.x\sqrt{1+m^2}\right|_{k_1}^{k_2}=?$
If you were to create a slope triangle for the points $(k_1, k_1m + b)$ and $(k_2, k_2m + b)$, what would be the length of each leg of the slope triangle?
$\sqrt{(k_2-k_1)^2+((k_2m+b)-(k_1m+b))^2}$