To create a graph representing the amount of money Dara has saved from the time she begins saving until she has saved enough for the bike, we will first calculate the total time it will take her to reach her savings goal and then plot the points accordingly.
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Determine Total Savings Goal:
- Dara needs $180 for the bicycle.
- She already has $30.
- Therefore, the amount she still needs to save is: \[ 180 - 30 = 150 \text{ dollars} \]
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Calculate the time it takes to save this amount:
- Dara saves $25 per week.
- To find out how many weeks it will take her to save $150, we divide: \[ \frac{150}{25} = 6 \text{ weeks} \]
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Plotting Points:
- At week 0, she has $30 saved. (Point: (0, 30))
- At week 1, she saves an additional $25: \[ 30 + 25 \cdot 1 = 55 \text{ dollars} \quad \text{(Point: (1, 55))} \]
- At week 2: \[ 30 + 25 \cdot 2 = 80 \text{ dollars} \quad \text{(Point: (2, 80))} \]
- At week 3: \[ 30 + 25 \cdot 3 = 105 \text{ dollars} \quad \text{(Point: (3, 105))} \]
- At week 4: \[ 30 + 25 \cdot 4 = 130 \text{ dollars} \quad \text{(Point: (4, 130))} \]
- At week 5: \[ 30 + 25 \cdot 5 = 155 \text{ dollars} \quad \text{(Point: (5, 155))} \]
- At week 6, she finally reaches her goal: \[ 30 + 25 \cdot 6 = 180 \text{ dollars} \quad \text{(Point: (6, 180))} \]
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Coordinates for the Graph:
- (0, 30)
- (1, 55)
- (2, 80)
- (3, 105)
- (4, 130)
- (5, 155)
- (6, 180)
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Graphing the Points:
- You will plot the points on a graph with:
- The horizontal axis (x-axis) representing time in weeks (0 to 6).
- The vertical axis (y-axis) representing the total amount saved in dollars (30 to 180).
- You will plot the points on a graph with:
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Connecting the Dots:
- Connect each of the plotted points with a straight line to represent her savings over time. The line will start at (0, 30) and go through each subsequent point until (6, 180).
This graph visually represents Dara's savings progression and shows how her savings grow as she continues to save $25 each week.
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