Question

the graph shows the number of possible passengers for a given number of roller - coaster cars that leave the platform. complete parts a and b.
view an example
video
get more help
clear all
check answer
m=
24 - 16
3 - 2
=
0
1
y=
0
x
(simplify your answers. use integers or fractions for any numbers in the expression.)
b. interpret the equation in words.
each roller - coaster car holds
passengers.
(type a whole number.)

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here \(x_1 = 16,y_1 = 0,x_2=24,y_2 = 4\). So \(m=\frac{4 - 0}{24 - 16}=\frac{4}{8}=\frac{1}{2}\). But from the given \(m=\frac{24 - 16}{3 - 2}\), there is a mistake. The correct slope - intercept form \(y=mx + b\). Since the line passes through \((0,0)\) (when \(x = 0\) cars, \(y=0\) passengers), \(b = 0\). The equation of the line is \(y=\frac{1}{2}x\).

Step2: Find the number of passengers per car

In the equation \(y=\frac{1}{2}x\), when \(x = 1\) (one roller - coaster car), \(y=\frac{1}{2}\times1 = 2\) (by cross - multiplying from the proportion \(\frac{y}{x}=\frac{4}{24 - 16}\), \(\frac{y}{1}=\frac{4}{2}\), \(y = 2\))

Answer:

a. Each roller - coaster car holds \(2\) passengers.
b. The equation \(y = 2x\) means that the number of passengers \(y\) is twice the number of roller - coaster cars \(x\). For example, if there are \(x\) cars, the number of passengers \(y\) can be found by multiplying the number of cars by \(2\).