This table gives a few 
\[(x,y)\] pairs of a line in the coordinate plane.
\[x\]	
\[y\]
\[32\]	
\[22\]
\[48\]	
\[17\]
\[64\]	
\[12\]
What is the 
\[y\]-intercept of the line?
\[(\]
\[,\]
\[)\]

To find the \(y\)-intercept of the line, we first need to determine the equation of the line in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.

### Step 1: Find the slope (\(m\)) of the line
The slope of a line is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((32, 22)\) and \((48, 17)\):

\[
m = \frac{17 - 22}{48 - 32} = \frac{-5}{16}
\]

Thus, the slope \(m = -\frac{5}{16}\).

### Step 2: Use the slope to find the \(y\)-intercept (\(b\))
Now that we know the slope, we can use one of the given points to solve for \(b\). Let's use the point \((32, 22)\) and substitute into the equation \(y = mx + b\):

\[
22 = -\frac{5}{16} \times 32 + b
\]

Simplify:

\[
22 = -10 + b
\]

Solve for \(b\):

\[
b = 22 + 10 = 32
\]

### Step 3: Write the equation of the line
The equation of the line is:

\[
y = -\frac{5}{16}x + 32
\]

Thus, the \(y\)-intercept is \(32\), and the \(y\)-intercept point is \((0, 32)\).

---

Do you need any further clarification on this?

### Related Questions:
1. How do you calculate the slope between two points?
2. Can you verify the slope using the points \((48, 17)\) and \((64, 12)\)?
3. How would the equation change if the slope was positive instead of negative?
4. What does the \(y\)-intercept represent graphically in the coordinate plane?
5. Can you find the equation of a line given a different pair of points?

**Tip**: To quickly find the slope between two points, remember to subtract the \(y\)-values and divide by the difference in \(x\)-values.

This table gives a few (x, y) pairs of a line in the coordinate plane. x: 32, y: 22; x: 48, y: 17; x: 64, y: 12. What is the y-intercept of the line?

Learn how to find the y-intercept of a line from a set of (x, y) pairs: (32, 22), (48, 17), and (64, 12). This problem uses the slope formula and slope-intercept form to determine the equation of the line. Ideal for students in Grades 8-10.

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