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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.

Use the graph to write an equation of the line.

Learn how to write the equation of a line based on a graph. The graph shows a savings account balance over time, and we calculate the slope and y-intercept to form the equation. Suitable for Grades 7-9 students learning algebra and linear equations.

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