Question

The amount of money earned for hours spent babysitting is displayed on the graph. Derive the equation of the line through the origin.
Layla's Babysitting Money
Y Axis
Money Earned ($) 22.00
16.50
11.00
5.50

1 2 3 4 5 X Axis
Hours worked

A. Y= $11x
B. Y= $5.50x
C. Y= $22x
D. Y= $16.50x

Answer 1

To derive the equation of a line through the origin, we can use the formula \( Y = mx \), where \( m \) is the slope, which represents the amount of money earned per hour.

From the graph, we can observe the points where Layla earns her money:

- At 1 hour, she earns $5.50.
- At 2 hours, she earns $11.00.
- At 3 hours, she earns $16.50.
- At 4 hours, she earns $22.00.

To find the slope \( m \), we can calculate it from the first point (1 hour, $5.50):

\[
m = \frac{\text{Money Earned}}{\text{Hours Worked}} = \frac{5.50}{1} = 5.50
\]

This means Layla earns $5.50 per hour. Thus, the equation can be represented as:

\[
Y = 5.50x
\]

This indicates the relationship between the hours worked (x) and the money earned (Y).

However, looking at the provided options again:

- A. \( Y = $11x \)
- B. \( Y = $5.50x \)
- C. \( Y = $22x \)
- D. \( Y = $16.50x \)

The correct option that matches our calculation of the slope is:

**B. Y = $5.50x**.