The graph shows a straight line, and the task is to find which equation from the list matches the line. To determine the correct equation, we need to consider two key characteristics:

1. Slope (m): The steepness or incline of the line.
2. y-intercept (b): The point where the line crosses the y-axis.

Observing the graph:

• The line crosses the y-axis at $y = -1$, so the y-intercept is $b = -1$.
• The slope $m$ can be calculated by observing the rise over run between two points on the line. For instance, if the line rises by 2 units and runs 1 unit to the right, the slope is $m = 2$.

Comparing to the given equations:

From the provided options:

• (a) $y = x - 3$ has a slope of 1 and a y-intercept of -3.
• (b) $y = 2x + 5$ has a slope of 2 and a y-intercept of 5.
• (c) $y = 10x$ has a slope of 10 and a y-intercept of 0.
• (d) $y = 2x - 1$ has a slope of 2 and a y-intercept of -1.
• (e) $y = 3x - 3$ has a slope of 3 and a y-intercept of -3.

Conclusion:

The equation that best matches the graph is d. $y = 2x - 1$ because the slope is 2, and the y-intercept is -1.

Would you like further explanation or details on how I calculated this?

Here are 5 related questions to expand your understanding:

1. What is the general form of a linear equation, and how do you identify slope and y-intercept?
2. How can you calculate the slope from two points on a graph?
3. What are the properties of lines with different slopes (positive, negative, zero)?
4. How does shifting the y-intercept change the position of the line on the graph?
5. Can you think of a real-world scenario where slope and intercept are useful?

Tip: Always remember, the slope tells you how steep the line is, and the y-intercept tells you where it crosses the y-axis.