The image displays a "Match the Equation to the Graph" activity with linear equations and corresponding graphs. To solve this:

1. Analyze the graphs: Identify slopes and y-intercepts for each graph.
2. Match equations: Compare with the given equations.

Let’s determine the matches based on the features:

Key features to identify:

• Slope (m): Look at how steep the graph is. Positive slopes go upwards, negative slopes downwards.
• Y-intercept (b): Find where the line crosses the y-axis (x=0).
• Vertical/Horizontal Lines: "x=a" is vertical, and "y=b" is horizontal.

Here’s the process:

Step-by-step Matching:

1. Graph 1: Appears to have a slope of 1/2 and a y-intercept of -3 → Equation: y = (1/2)x - 3.

2. Graph 2: Appears to have a slope of -2 and a y-intercept of -4 → Equation: y = -2x - 4.

3. Graph 3: A horizontal line at y = 3 → Equation: y = 3.

4. Graph 4: A vertical line at x = 3 → Equation: x = 3.

5. Graph 5: Appears to have a slope of -3/2 and a y-intercept of -8 → Equation: y = -(3/2)x - 8.

6. Graph 6: Appears to have a slope of 3/2 and a y-intercept of 8 → Equation: y = (3/2)x + 8.

Would you like further details on graph features or a specific explanation for each match?

Relative Questions:

1. What is the difference between positive and negative slopes?
2. How can you identify a vertical line equation?
3. Why does the y-intercept occur at $x = 0$?
4. How do you calculate the slope from a graph?
5. What happens to the graph when only the slope changes?

Tip:

Always start with the y-intercept to narrow down the equation possibilities quickly.