The given equation is $y = -\frac{1}{2}x + 3$. This represents a linear equation in slope-intercept form $y = mx + b$, where:

• $m = -\frac{1}{2}$ is the slope.
• $b = 3$ is the y-intercept, which means the line crosses the y-axis at $y = 3$.

Steps to graph the line:

1. Plot the y-intercept (0, 3): Start by plotting the point where the line crosses the y-axis. This is the point $(0, 3)$.

2. Use the slope to find another point: The slope $-\frac{1}{2}$ means that for every 2 units you move to the right (positive direction of x-axis), you move 1 unit down (since the slope is negative). Starting from $(0, 3)$, move:

   • 2 units to the right to $x = 2$,
   • 1 unit down to $y = 2$.

   This gives you a second point: $(2, 2)$.

3. Draw the line: Now, draw a straight line passing through the points $(0, 3)$ and $(2, 2)$. You can extend this line in both directions.

Would you like more details or have any questions?

Here are five related questions for further practice:

1. What is the slope of the line $y = \frac{2}{3}x - 1$?
2. How would you graph the equation $y = -3x + 5$?
3. What does it mean if a line has a slope of zero?
4. How do you determine the x-intercept of a line?
5. How does changing the slope affect the steepness of a line?

Tip: The slope $m$ tells you how the line rises or falls as you move along the x-axis.