Question

1. analyze and persevere are the steepest parts of the two water slides parallel? explain
2. mathematical connections teo rides his bike in a straight line from his location, perpendicular to path a, and luke rides his bike in a straight line from his location, perpendicular to path b. what are the coordinates of the point where they meet?

Explanation:

Step1: Determine the slope - intercept form for slide 1

The slope $m_1$ of a line is given by $m=\frac{\text{rise}}{\text{run}}$. For slide 1, rise = 72 ft and run = 40 ft, so $m_1=\frac{72}{40}=\frac{9}{5}$.

Step2: Determine the slope - intercept form for slide 2

For slide 2, rise = 40 ft and run = 24 ft, so $m_2=\frac{40}{24}=\frac{5}{3}$.
Since $m_1
eq m_2$, the two water - slides are not parallel.

For problem 27:

Step1: Identify Teo's and Luke's starting points

Teo's starting point is $(2,2)$ and Luke's starting point is $(9,8)$.

Step2: Analyze the perpendicular paths

Teo moves perpendicular to path A and Luke moves perpendicular to path B. Looking at the grid, Teo will move vertically until he reaches the same y - coordinate as Luke, and Luke will move horizontally until he reaches the same x - coordinate as Teo.
The x - coordinate of the meeting point is 9 and the y - coordinate of the meeting point is 2.

Answer:

The two water - slides are not parallel because their slopes are different. For Teo and Luke, the coordinates of the meeting point are $(9,2)$.