Tara runs an amusement park ride and needs to count the people who get on the ride. At the beginning of her shift, 132 people had ridden the ride. This table shows the total number of riders for several times during Tara's shift.

Question

Hours into Tara's shift (x)

0 1 2 3
Total number of riders (y)

132 165 198 231
What is the equation in slope-intercept form that represents the total number of riders over time?

Choose the correct expressions from the drop-down menus to correctly complete the equation.

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Answer 1

To find the equation in slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

From the data provided:

• At \( x = 0 \), \( y = 132 \)
• At \( x = 1 \), \( y = 165 \)
• At \( x = 2 \), \( y = 198 \)
• At \( x = 3 \), \( y = 231 \)

First, we can find the slope \( m \) by examining the change in \( y \) over the change in \( x \).

From \( x = 0 \) to \( x = 1 \):

• Change in \( y = 165 - 132 = 33 \)
• Change in \( x = 1 - 0 = 1 \)

Thus, the slope \( m \) is: \[ m = \frac{33}{1} = 33 \]

Now, we already know the y-intercept \( b \) from the data at \( x = 0 \): \[ b = 132 \]

Putting it all together, the equation in slope-intercept form is: \[ y = 33x + 132 \]

So, the correct expressions to complete the equation are: \[ y = 33x + 132 \]