The graph shows a linear relationship between time (in weeks) and the balance (in dollars) in a savings account. We need to derive the equation of the line from the given points.

From the graph:

• One point is $(0, 100)$, indicating the initial balance (the y-intercept).
• Another point is $(4, 300)$, giving another reference.

Step 1: Calculate the slope of the line

The slope $m$ of a line is calculated using the formula:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Here, $(x_1, y_1) = (0, 100)$ and $(x_2, y_2) = (4, 300)$. Plugging in these values:

$m = \frac{{300 - 100}}{{4 - 0}} = \frac{200}{4} = 50$

Step 2: Write the equation in slope-intercept form

The slope-intercept form of a line is given by:

$y = mx + b$

Where:

• $m = 50$ (the slope)
• $b = 100$ (the y-intercept, from the point $(0, 100)$)

Thus, the equation of the line is:

$y = 50x + 100$

This represents the balance in the savings account as a function of time.

Would you like further details or clarifications? Here are five related questions to expand on this:

1. How do we interpret the slope of the line in this context?
2. What does the y-intercept represent in practical terms for this problem?
3. How would the equation change if the initial balance was higher?
4. What if we wanted to predict the balance after 6 weeks using this equation?
5. How could we calculate the time it takes for the balance to reach $500?

Tip: The slope of a line represents the rate of change, which in this case is how much the savings increase per week.