The equation $y = -\frac{1}{2}x + 4$ represents a straight line in slope-intercept form, which is $y = mx + b$, where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

For this specific equation:

• The slope $m = -\frac{1}{2}$, indicating that for every unit increase in $x$, $y$ decreases by $\frac{1}{2}$ units.
• The y-intercept $b = 4$, meaning the line crosses the y-axis at $y = 4$.

Properties of the Line:

• Slope: $-\frac{1}{2}$
• Y-intercept: $(0, 4)$
• X-intercept: Set $y = 0$ and solve for $x$.

To find the x-intercept: $0 = -\frac{1}{2}x + 4$ $\frac{1}{2}x = 4$ $x = 8$ So, the x-intercept is at $(8, 0)$.

Would you like to see the graph of this line or have any further details?

Here are 5 questions related to this concept:

1. How do you find the slope between two points on a line?
2. What is the significance of the y-intercept in a real-world scenario?
3. How would the line change if the slope were positive?
4. Can you write the equation of a line parallel to this one?
5. How do you determine if two lines are perpendicular?

Tip: The sign of the slope indicates the direction of the line; a negative slope means the line descends as it moves from left to right.