A line in the xy-plane passes through the points (0, 4) and (4, 2).\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{8}\]
\[\small{\llap{-}2}\]
\[y\]
\[x\]
\[O\]
What is the 
\[y\]-intercept of the line shown?

To find the \( y \)-intercept of the line passing through the points \( (0, 4) \) and \( (4, 2) \), we can follow these steps:

### Step 1: Understand the Equation of a Line
The general equation of a line in slope-intercept form is:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the line, and
- \( b \) is the \( y \)-intercept (the value of \( y \) when \( x = 0 \)).

### Step 2: Find the Slope \( m \)
The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated as:

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

For the points \( (0, 4) \) and \( (4, 2) \):

\[
m = \frac{2 - 4}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}
\]

### Step 3: Find the \( y \)-intercept
The \( y \)-intercept is the value of \( y \) when \( x = 0 \). In this case, one of the points given is \( (0, 4) \), which means the line passes through the point \( (0, 4) \). Therefore, the \( y \)-intercept is:

\[
b = 4
\]

### Conclusion
The \( y \)-intercept of the line is \( 4 \).

Would you like more details on this or have any questions?

Here are some related questions for further exploration:
1. What is the equation of the line passing through the points \( (0, 4) \) and \( (4, 2) \)?
2. How do you find the slope if the coordinates are negative?
3. What is the slope of a vertical line, and how does it affect the \( y \)-intercept?
4. How do we find the equation of a line given its slope and one point?
5. Can a line have more than one \( y \)-intercept?

**Tip**: When two points on a line are given, always find the slope first to help write the equation of the line!

A line in the xy-plane passes through the points (0, 4) and (4, 2). What is the y-intercept of the line shown?

Learn how to find the y-intercept of a line passing through the points (0, 4) and (4, 2) using the slope-intercept form. This example covers key concepts in coordinate geometry and is suitable for students in Grades 8-10.

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