From the image, it seems that the problem involves calculating the slope and the y-intercept of a line passing through two points, as well as interpreting the slope.

The given points are:

• $(2005, 23000)$
• $(2015, 35000)$

1. Slope $m$:

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values: $m = \frac{35000 - 23000}{2015 - 2005} = \frac{12000}{10} = 1200$

So, the slope $m = 1200$.

2. Y-intercept $(0, b)$:

To find the y-intercept, we use the equation of the line $y = mx + b$, where $b$ is the y-intercept. We already know the slope $m = 1200$ and can use one of the points, say $(2005, 23000)$, to solve for $b$:

$23000 = 1200(2005) + b$

First, calculate $1200 \times 2005$: $1200 \times 2005 = 2406000$

Now solve for $b$: $23000 = 2406000 + b \implies b = 23000 - 2406000 = -2383000$

So, the y-intercept is $(0, -2383000)$.

3. Slope-intercept form of the line:

The slope-intercept form of a line is given by: $y = mx + b$

Substitute $m = 1200$ and $b = -2383000$: $y = 1200x - 2383000$

4. Interpretation of the slope:

The slope $m = 1200$ means that the cost of tuition is increasing by $1200 per year, on average. Therefore, the correct interpretation is B: The cost is increased by $1200 per year, on average.

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. What is the significance of the y-intercept in this context?
2. How would the line change if the slope were negative?
3. What would be the new equation if the tuition in 2020 is projected to be $40,000?
4. How would you calculate the slope if only partial data was available?
5. What would the line look like if the tuition cost remained constant over time?

Tip: The slope of a line always represents the rate of change between two quantities. If it's positive, the dependent variable increases as the independent variable increases.