Let's break down and solve the problem shown in your image step by step:

Problem Description:

• The price of stock DDD is currently $15 per share.
• The price has been increasing by $1/2 (or $0.50) per week.
• You are asked to:
  1. Write an equation for the situation.
  2. Use that equation to complete a table of values.
  3. Graph the equation.

Part a) Writing the Equation:

Let:

• $x$ = weeks
• $y$ = price of the stock

The equation for this situation is a linear one, following the form $y = mx + b$, where $m$ is the slope (rate of increase) and $b$ is the initial price.

• The initial price (when $x = 0$) is $15, so $b = 15$.
• The rate of increase per week is $0.50, so $m = 0.5$.

Thus, the equation is: $y = 0.5x + 15$

Part b) Completing the Table:

Use the equation $y = 0.5x + 15$ to fill in the values of the table for each week.

1. For $x = 0$ (week 0): $y = 0.5(0) + 15 = 15$ So, the price is $15.

2. For $x = 2$ (week 2): $y = 0.5(2) + 15 = 1 + 15 = 16$ So, the price is $16.

3. For $x = 4$ (week 4): $y = 0.5(4) + 15 = 2 + 15 = 17$ So, the price is $17.

Now, the table looks like this:

Part c) Graphing the Equation:

To graph the equation $y = 0.5x + 15$:

• Start by plotting the points from the table: (0, 15), (2, 16), (4, 17).
• Draw a line through these points, extending in both directions to represent the stock price as time increases.

Would you like help graphing the equation, or any further explanation on these steps?

Follow-up questions:

1. How do we determine the slope in a linear equation?
2. What does the y-intercept represent in the context of this problem?
3. How would the equation change if the stock price was decreasing?
4. Can you predict the price at week 10 using the equation?
5. How would you describe the relationship between weeks and stock price?

Tip: When graphing a linear equation, it helps to plot at least two points and then extend the line through them!