n 2005 the average annual tuition and fees for attending a private college or university was ​$23 comma 000. This cost rose to about ​$35 comma 000 in 2015​, as illustrated in the graph. Complete parts a and b.
2005
2010
2015
2020
x
2000
y
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
Year
Cost (dollars)
left parenthesis 2005 comma 23000 right parenthesisleft parenthesis 2015 comma 35000 right parenthesis



The correlation grid has a horizontal x-axis ranging from 2000 to 2020 representing the year which starts from 2000. After 2000 the next tick is at the year labeled 2005, then it is labeled in the increments of 5. A vertical y-axis ranging from 0 to 40,000 is labeled in the increments of 5,000 representing the cost in dollars. The graph has a line segment that connects the points (2005,23000) and (2015,35000).
Question content area bottom
Part 1
a. Find the​ slope-intercept form of the line passing through ​(2005​,23000​) and ​(2015​,35000​). 

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:

\[
y = 1200x - 2383000
\]

---

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.

In 2005, the average annual tuition and fees for attending a private college or university was $23,000. This cost rose to about $35,000 in 2015, as illustrated in the graph. Complete parts a and b. Part 1 a. Find the slope-intercept form of the line passing through (2005, 23000) and (2015, 35000).

Learn how to find the slope-intercept form of a line passing through the points (2005, 23000) and (2015, 35000). This algebra problem involves calculating the slope and using the point-slope form to determine the equation of the line. Suitable for students in Grades 9-11.

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