To solve this problem, we need to find the equation of the line in slope-intercept form, which is given by:

$y = mx + b$

Here, $m$ is the slope, and $b$ is the y-intercept (the point where the line crosses the y-axis).

Step 1: Determine the slope ($m$)

To calculate the slope, we use the formula:

$m = \frac{{\text{rise}}}{{\text{run}}}$

By observing the graph, we can see two points where the line crosses grid intersections. Let's assume the line passes through the points:

1. $(-2, -3)$
2. $(0, -1)$

Using these points, the rise (change in y) is:

$\text{rise} = -1 - (-3) = 2$

The run (change in x) is:

$\text{run} = 0 - (-2) = 2$

Thus, the slope is:

$m = \frac{2}{2} = 1$

Step 2: Find the y-intercept ($b$)

The line crosses the y-axis at the point $(0, -1)$, which means the y-intercept $b$ is $-1$.

Step 3: Write the equation

Substituting the slope ($m = 1$) and y-intercept ($b = -1$) into the slope-intercept form:

$y = 1x - 1 \quad \text{or simply} \quad y = x - 1$

Conclusion:

The correct equation is not listed among the given choices. The correct equation should be:

$y = x - 1$

Would you like more details or have any questions?

5 Related Questions:

1. How do you find the slope of a line from a graph?
2. What is the importance of the y-intercept in the equation of a line?
3. How do you recognize when a line has a negative slope?
4. How would the equation change if the line had a steeper slope?
5. What are the different forms of a line's equation besides slope-intercept?

Tip:

When finding the slope from a graph, always pick two clear points that lie exactly on the grid lines for accurate calculation!