Let's go through each part of the worksheet you provided.

1. Graph Interpretation

• First graph:

  • Slope $m = -1$ (since the line goes down 1 unit for every 1 unit to the right).
  • $y$-intercept $b = -3$ (where the line crosses the $y$-axis at $y = -3$).

• Second graph:

  • Slope $m = \frac{4}{3} \approx 1.33$ (since the line goes up by 4 units for every 3 units to the right).
  • $y$-intercept $b = 4$ (where the line crosses the $y$-axis at $y = 4$).

2. Tables Interpretation

For the two tables provided:

• Third table (with values $x: 0, 3, 6, 9, 12$ and $y: 10, 19, 28, 37$):

  • To find the slope $m$, use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
  • Between points $(0, 10)$ and $(3, 19)$, the slope is: $m = \frac{19 - 10}{3 - 0} = \frac{9}{3} = 3$
  • The $y$-intercept $b$ is 10 (since $y = 10$ when $x = 0$).

• Fourth table (with values $x: 0, 2, 4, 6, 8$ and $y: 0, 2, 3, 4, 5$):

  • Using the same slope formula between points $(0, 0)$ and $(2, 2)$: $m = \frac{2 - 0}{2 - 0} = 1$
  • The $y$-intercept $b = 0$ (since $y = 0$ when $x = 0$).

3. Pizza Cost Problem

The equation given is $C = 2t + 8$, where:

• $C$ is the total cost of the pizza.
• $t$ is the number of toppings.

The slope $m = 2$ represents the cost of each additional topping (since each topping adds $2). The $y$-intercept $b = 8$ represents the base price of the pizza without any toppings ($8).

For a graph:

• When $t = 0$ (no toppings), $C = 8$.
• When $t = 1$, $C = 2(1) + 8 = 10$.
• When $t = 2$, $C = 2(2) + 8 = 12$, and so on.

Would you like me to expand or clarify any part of the explanation?

Here are five related questions to deepen your understanding:

1. What does it mean when a line has a negative slope?
2. How does the value of the slope affect the steepness of a line?
3. How can you quickly find the y-intercept from a graph?
4. What real-world situations can be modeled with linear equations like the pizza problem?
5. How does the number of toppings affect the slope in the pizza problem?

Tip: To identify the slope visually, remember that "rise over run" is the key — how much the line goes up or down (rise) for a given horizontal distance (run).