https://r2.erweima.ai/mathbot/image/1726649602986cb0iiccw.jpg

The problem asks to find the formula for line \( a \) based on the given graph.

1. The provided formula in the image is \( k = 20 + 2b \), which represents the red line in the graph. This is a linear equation where:
   - The slope (rate of change of \( k \) with respect to \( b \)) is 2.
   - The intercept on the \( k \)-axis is 20, meaning when \( b = 0 \), \( k = 20 \).

2. Now, line \( a \) is a horizontal line on the graph, and it crosses the \( k \)-axis at \( k = 30 \).

Since line \( a \) is horizontal, its slope is 0. This means that the value of \( k \) is constant regardless of \( b \).

### The equation for line \( a \) is simply:
\[
k = 30
\]
This represents the constant value of \( k \) along line \( a \).

Would you like more details or have any questions about this explanation?

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Here are five related questions to deepen your understanding:

1. How do you determine the slope of a line from its equation?
2. What is the significance of the \( b \)-intercept in the equation \( k = 20 + 2b \)?
3. How can you find the equation of a line if you know its slope and one point on it?
4. What would the graph look like if the slope of the line were negative instead of positive?
5. How can you identify the intersection points between two lines on a graph?

**Tip:** For any horizontal line, the slope is always zero, and its equation is simply \( y = c \), where \( c \) is the constant value along the \( y \)-axis.

Learn how to find the equation of a horizontal line on a graph. This example covers linear equations, slopes, and intercepts, focusing on finding the formula for line a, which is a horizontal line where k = 30.

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