To determine which graph represents the equation $y = -\frac{1}{2}x + 3$, we need to analyze the characteristics of this equation. This equation is in slope-intercept form, $y = mx + b$, where:

• $m = -\frac{1}{2}$ is the slope, indicating a downward slope of 1 unit for every 2 units moved to the right.
• $b = 3$ is the y-intercept, meaning the line crosses the y-axis at $y = 3$.

Based on this information, we expect the correct graph to:

1. Pass through the point (0, 3) on the y-axis.
2. Have a downward slope, falling half a unit in $y$ for every full unit in $x$.

Now, looking at the four graph options provided in the second image:

• The correct graph should show a line that intersects the y-axis at $y = 3$ and has a negative slope.

Observing the options, the graph in the top left corner best matches these characteristics, as it has a negative slope and crosses the y-axis at $y = 3$.

Thus, the answer to question 10 is likely the top left graph (option corresponding to that position).

Would you like further clarification on any steps, or do you have other questions?

Here are five related questions for further exploration:

1. How would the graph change if the slope were positive?
2. What effect would changing the y-intercept to 5 have on the graph?
3. How do you determine the slope from two points on a line?
4. How can you identify the y-intercept of a line from its graph?
5. How would you graph $y = \frac{1}{2}x - 3$ on the same axes?

Tip: Always start by plotting the y-intercept first, then use the slope to determine the direction and steepness of the line.