Question

On the y axis the numbers are: 10,20,30,40,50,60,70,80, and 90 On the x axis the numbers are: 1,2,3,4,5,6,7,8,9, and 10. The y intercept is 30, and the slope is positive. If juan starts with $30 in his savings, how much does his savings amount increase each week. The x axis represents time and the y represents the amount of money

Answer 1

To determine how much Juan's savings increase each week, we need to analyze the information given about the graph.

1. The y-intercept is 30, which means that at time $x=0$ (the start), Juan has $30.
2. The slope of the line is positive, which indicates that his savings are increasing over time.
3. 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:

$$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{40-30}{1-0}=\frac{10}{1}=10$$

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.