To find the slope-intercept form of the line passing through the points $(2005, 23000)$ and $(2015, 35000)$, we will follow these steps:

Step 1: Calculate the slope (m)

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

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

Substitute the given points $(2005, 23000)$ and $(2015, 35000)$:

$m = \frac{35000 - 23000}{2015 - 2005} = \frac{12000}{10} = 1200$

Step 2: Use the point-slope form of the equation

The point-slope form of the equation of a line is:

$y - y_1 = m(x - x_1)$

We can use either of the given points; let's use $(2005, 23000)$:

$y - 23000 = 1200(x - 2005)$

Step 3: Simplify into slope-intercept form

We now simplify this equation to get it into the slope-intercept form $y = mx + b$:

$y - 23000 = 1200(x - 2005)$ $y - 23000 = 1200x - 1200 \times 2005$ $y - 23000 = 1200x - 2406000$ $y = 1200x - 2406000 + 23000$ $y = 1200x - 2383000$

Thus, the equation of the line in slope-intercept form is:

$y = 1200x - 2383000$

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Would you like to go over the steps in more detail or have any questions?

Follow-up questions:

1. How do you interpret the slope in this context?
2. Can you determine the cost in 2020 using this equation?
3. What would the tuition cost have been in 2010 according to this model?
4. How would the line change if the tuition increased at a slower rate?
5. What does the y-intercept $-2383000$ represent in this context?

Tip: The slope represents the rate of change; in this case, how much the tuition increases per year.