CPM Homework Help : APCALC Problem 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.

Step 1:

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

Step 2:

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

Using the Pythagorean Theorem:

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?

Step:

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