The problem asks to model the situation using a linear equation in slope-intercept form. The equation should relate $x$ (the number of weeks) to $p$ (the price of the stock).

Given:

• The initial price of the stock (at $x = 0$) is $45.
• After 4 weeks (at $x = 4$), the price is $53.

The general slope-intercept form of a line is: $p = mx + b$ where:

• $m$ is the slope (rate of change),
• $b$ is the y-intercept (initial price at $x = 0$).

Step 1: Calculate the slope

The slope $m$ is given by the rate of change in price per week, calculated as: $m = \frac{\Delta p}{\Delta x} = \frac{53 - 45}{4 - 0} = \frac{8}{4} = 2$

So, the slope is $m = 2$. This means the price increases by $2 per week.

Step 2: Write the equation

Since the initial price (y-intercept) is $45, the equation becomes: $p = 2x + 45$

Thus, the equation modeling the situation is: $p = 2x + 45$

This equation shows that the stock price increases by $2 each week starting from $45.

Would you like further clarification, or have any other questions?

Here are 5 related questions:

1. How would the equation change if the price started at $50 instead of $45?
2. What happens to the slope if the price increases by $3 per week?
3. Can you determine how many weeks it would take for the stock price to reach $65?
4. How would the graph of this equation look, and where would it intercept the axes?
5. What is the significance of the slope and y-intercept in practical terms?

Tip: When determining the slope of a line, think of it as the rate of change per unit, which in this case is the change in stock price per week.