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.
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.
Answers
GPT-4o mini
To graph the relationship between the time Jim spends babysitting (x) and the amount he earns (y), we will use the equation for a proportional relationship, which is:
\[ y = kx \]
where \( k \) is the constant of proportionality (in this case, Jim's hourly rate).
Since Jim earns $12 per hour, we can set \( k = 12 \). Thus, the equation becomes:
\[ y = 12x \]
### Select Points
Now, let's select two points to plot on the graph. We can choose values for \( x \) (the number of hours), and then calculate \( y \) (the money earned).
1. **First Point:**
- Choose \( x = 2 \) hours:
\[ y = 12 \times 2 = 24 \]
- This gives us the point (2, 24).
2. **Second Point:**
- Choose \( x = 5 \) hours:
\[ y = 12 \times 5 = 60 \]
- This gives us the point (5, 60).
### Points Summary
The two points we selected are:
- Point 1: (2, 24)
- Point 2: (5, 60)
### Graphing the Points
To graph the relationship, you can plot the selected points on a coordinate plane where:
- The x-axis represents the time in hours (x), and
- The y-axis represents the money earned in dollars (y).
1. Plot the point (2, 24).
2. Plot the point (5, 60).
3. Draw a straight line through these points to represent the proportional relationship.
The line should extend infinitely in both directions, as the relationship continues to hold for any number of hours Jim babysits.
\[ y = kx \]
where \( k \) is the constant of proportionality (in this case, Jim's hourly rate).
Since Jim earns $12 per hour, we can set \( k = 12 \). Thus, the equation becomes:
\[ y = 12x \]
### Select Points
Now, let's select two points to plot on the graph. We can choose values for \( x \) (the number of hours), and then calculate \( y \) (the money earned).
1. **First Point:**
- Choose \( x = 2 \) hours:
\[ y = 12 \times 2 = 24 \]
- This gives us the point (2, 24).
2. **Second Point:**
- Choose \( x = 5 \) hours:
\[ y = 12 \times 5 = 60 \]
- This gives us the point (5, 60).
### Points Summary
The two points we selected are:
- Point 1: (2, 24)
- Point 2: (5, 60)
### Graphing the Points
To graph the relationship, you can plot the selected points on a coordinate plane where:
- The x-axis represents the time in hours (x), and
- The y-axis represents the money earned in dollars (y).
1. Plot the point (2, 24).
2. Plot the point (5, 60).
3. Draw a straight line through these points to represent the proportional relationship.
The line should extend infinitely in both directions, as the relationship continues to hold for any number of hours Jim babysits.