### Home > APCALC > Chapter 10 > Lesson 10.1.8 > Problem10-99

10-99.

What is the arc length of the curve $y = mx + b (m ≠ 0)$ from $x = k_l$ to $x = k_2 (k_l < k_2)$? Use the arc length formula. Then verify your result using the Pythagorean Theorem. Illustrate your work with a diagram.

$\text{arc length = }\int_{k_1}^{k_2}\sqrt{1+m^2}dx$

$=\left.x\sqrt{1+m^2}\right|_{k_1}^{k_2}=?$

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?

$\sqrt{(k_2-k_1)^2+((k_2m+b)-(k_1m+b))^2}$