To find the slope-intercept form of the equation $y = mx + b$ that models this linear relationship, we can examine the data provided:

Step 1: Determine the Slope (m)

The slope $m$ represents the rate of change in cost with each additional movie streamed. We can calculate $m$ by using two data points from the table.

Let’s use the points $(2, 14)$ and $(4, 17)$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{17 - 14}{4 - 2} = \frac{3}{2} = 1.5$

Thus, the slope $m$ is 1.5, indicating that each additional movie costs $1.50.

Step 2: Determine the Y-intercept (b)

The y-intercept $b$ represents the base fee, or the cost when no movies are streamed. We can use the slope-intercept form $y = mx + b$ and substitute one of the points to solve for $b$.

Using the point $(2, 14)$: $14 = 1.5(2) + b$ $14 = 3 + b$ $b = 11$

So, the y-intercept $b$ is 11, indicating a base membership fee of $11.

Final Equation

The equation in slope-intercept form is: $y = 1.5x + 11$

This equation models the linear relationship between the number of movies streamed and the total cost.

Would you like more details on any of the steps? Here are some related questions for deeper understanding:

1. How can we interpret the slope in terms of this streaming service’s charges?
2. How would the equation change if the cost per movie were different?
3. What would the cost be for streaming 10 movies in a month?
4. How can we use this equation to determine the base membership fee if it’s unknown?
5. How does the y-intercept reflect the monthly fee even when no movies are streamed?

Tip: The slope $m$ in a linear equation always represents the rate of change, which in real-world scenarios can show cost per unit, speed, or other per-unit changes.