Question

2 the graph shows the relationship between the number of cars on a rollercoaster (y) and the corresponding number of wheels (x). a what is the slope of this line? interpret this value in the context of this problem. b will this line pass through the point (108, 18)? explain why or why not.

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $y=\frac{1}{6}x$, the slope $m=\frac{1}{6}$.

Step2: Interpret the slope

In the context of the problem, where $y$ is the number of cars on a roller - coaster and $x$ is the number of wheels, the slope $\frac{1}{6}$ means that for every 6 wheels, there is 1 car on the roller - coaster.

Step3: Check if the point lies on the line

Substitute $x = 108$ and $y = 18$ into the equation $y=\frac{1}{6}x$.
When $x = 108$, $y=\frac{1}{6}\times108=18$. Since the left - hand side ($y = 18$) is equal to the right - hand side ($\frac{1}{6}\times108 = 18$), the line passes through the point $(108,18)$.

Answer:

a. The slope of the line is $\frac{1}{6}$. It means that for every 6 wheels, there is 1 car on the roller - coaster.
b. Yes, the line will pass through the point $(108,18)$ because when $x = 108$, $y=\frac{1}{6}\times108 = 18$.