The image shows a graph with a straight line and a multiple-choice question asking which equation represents the graph. The options are:

A) $y = \frac{1}{2}x + 6$
B) $y = \frac{1}{2}x - 2$
C) $y = -\frac{1}{2}x + 6$
D) $y = -\frac{1}{3}x - 2$

Steps to Identify the Correct Equation:

1. Slope of the Line: The line has a positive slope (it's rising from left to right), which means the coefficient of $x$ in the equation must be positive.

2. Y-Intercept: The y-intercept is the point where the line crosses the y-axis. We can estimate it visually:

   • The line appears to cross the y-axis slightly above the origin (0, -2), indicating the y-intercept is negative.

3. Matching the Equation:

   • Since the slope is positive, the correct equation must have a positive coefficient for $x$, ruling out options C and D.
   • The y-intercept is approximately -2, which corresponds with option B: $y = \frac{1}{2}x - 2$.

Answer:

The correct equation that represents the graph is Option B: $y = \frac{1}{2}x - 2$.

Would you like more details on how to analyze these types of problems or have any other questions?

Relative Questions:

1. How can you determine the slope of a line from a graph?
2. What is the significance of the y-intercept in a linear equation?
3. How do you identify if the slope of a line is positive or negative by looking at a graph?
4. What steps can be taken to solve for the equation of a line given two points?
5. How would the graph change if the slope of the line was negative?

Tip:

When identifying the equation of a line from a graph, always check the slope (whether the line is ascending or descending) and the y-intercept (where the line crosses the y-axis). These two key features will help you quickly match the correct equation.