Question

Jim is saving up to buy a new remote-controlled car, so he starts babysitting for his neighbors on weekends. He earns $12 per hour babysitting.
There is a proportional relationship between x, the time (in hours) that Jim spends babysitting, and y, the amount of money he earns (in dollars).
Graph this relationship. Select two points to draw a line. it only goes up to 20

Answer 1

To graph the relationship between the time Jim spends babysitting (x) and the amount of money he earns (y), we can create a table of values based on his hourly wage of $12.

Here's how the relationship looks mathematically:

\[ y = 12x \]

### Create Points

Let's calculate the earnings for a few values of x (time in hours):

- If Jim works 0 hours:
- \( y = 12 \times 0 = 0 \)
- Point: (0, 0)

- If Jim works 1 hour:
- \( y = 12 \times 1 = 12 \)
- Point: (1, 12)

- If Jim works 2 hours:
- \( y = 12 \times 2 = 24 \)
- Point: (2, 24)

- If Jim works 3 hours:
- \( y = 12 \times 3 = 36 \)
- Point: (3, 36)

Since the maximum value is 20 for this graph, we will only plot points where \( y \) does not exceed 20.

### Select Two Points

For our graph, we can use the following points within the limit of y = 20:

1. (0, 0)
2. (1, 12)

### Graphing

1. Plot the points (0, 0) and (1, 12) on a coordinate graph.
2. Draw a straight line through these points, extending it horizontally until it approaches (2, 24) but only visually illustrating up to y = 20.

### Summary

- The points selected for the graph are: (0, 0) and (1, 12).
- You can see that as Jim spends more time babysitting, his earnings increase proportionally based on the relationship \( y = 12x \).

If you have graph paper or a graphing software, you can plot these points and draw the line accordingly.