The function \( g(x) = -\frac{1}{2}x + 1 \) is a linear equation. Let's break it down:

1. **Slope (m):** The coefficient of \( x \) is \( -\frac{1}{2} \), which means the slope of the line is \( -\frac{1}{2} \). A negative slope indicates the line is decreasing, meaning it slopes downwards as \( x \) increases.

2. **Y-intercept (b):** The constant term is \( 1 \), so the y-intercept is \( 1 \). This is the point where the line crosses the y-axis, specifically at \( (0, 1) \).

In summary, the line described by this function:
- Decreases by \( \frac{1}{2} \) unit for every 1 unit increase in \( x \),
- Passes through the point \( (0, 1) \) on the y-axis.

### Do you want more details, or do you have any questions?

Here are 5 related questions to explore:

1. What is the graph of \( g(x) = -\frac{1}{2}x + 1 \)?
2. How do you find the x-intercept of \( g(x) = -\frac{1}{2}x + 1 \)?
3. What happens to the graph if you change the slope to \( -1 \) instead of \( -\frac{1}{2} \)?
4. How would the graph change if the y-intercept were \( 2 \) instead of \( 1 \)?
5. What is the value of \( g(x) \) when \( x = 4 \)?

**Tip:** The slope \( m \) controls how steep the line is, and the sign of \( m \) determines the direction it tilts.

Explore how to solve and interpret the linear equation g(x) = -1/2x + 1. This problem involves key concepts such as slope and y-intercept, explaining how the line decreases with a slope of -1/2 and crosses the y-axis at (0,1). Perfect for students in Grades 8-10.

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