To determine how much Juan's savings increase each week, we need to analyze the information given about the graph.
- The y-intercept is 30, which means that at time \(x = 0\) (the start), Juan has $30.
- The slope of the line is positive, which indicates that his savings are increasing over time.
- The values on both axes suggest that each unit increase on the x-axis represents one week, and each unit increase on the y-axis represents an increase in savings.
Based on the y-axis values of 10, 20, 30, ..., 90, we can assume that every unit on the y-axis represents an increase of $10. Therefore, the total increase in savings from the y-intercept 30 to a subsequent y-value can be calculated as follows:
Given that the slope is positive and it is a straight line, we can denote the slope \(m\) as the change in y divided by the change in x, which illustrates how much the savings increase each week.
For example, if we assume that the line connects two points (at \(x = 0\), \(y = 30\) and at some other \(x = 1\), \(y = 40\)), the slope \(m\) would be calculated as:
\[ m = \frac{\Delta y}{\Delta x} = \frac{40 - 30}{1 - 0} = \frac{10}{1} = 10 \]
Thus, if the savings increase by $10 for each week, this confirms that we have a slope of 10. Juan's savings amount increases by $10 each week.
If we wanted to confirm this, we could consider other y-values up to a maximum of 90:
- If after 1 week (x = 1), savings would be $40
- After 2 weeks (x = 2), it would be $50
- This pattern continues up to 10 weeks where savings would be $90.
In conclusion, Juan's savings increase by $10 each week.
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