The new image shows a graph with a linear equation plotted on a coordinate plane. The line passes through two points, which we can use to determine the slope-intercept form of the equation.

Step 1: Identify two points on the line.

From the graph:

• One point seems to be at $(0, -1)$, which is the y-intercept.
• Another point appears to be at $(2, 1)$.

Step 2: Calculate the slope $m$.

The slope $m$ is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(x_1, y_1) = (0, -1)$ and $(x_2, y_2) = (2, 1)$: $m = \frac{1 - (-1)}{2 - 0} = \frac{2}{2} = 1$

Step 3: Write the slope-intercept form equation.

The slope-intercept form is: $y = mx + b$ Where $m = 1$ and $b = -1$. Thus, the equation is: $y = x - 1$

This is the equation of the line in slope-intercept form.

Would you like more details on any specific part of this process, or do you have any further questions?

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Here are 5 questions related to this explanation:

1. What happens to the slope-intercept form if the slope $m$ is negative?
2. How do you find the slope if the points are far apart on the graph?
3. What is the slope of a horizontal line, and how does that affect the equation?
4. Can the y-intercept ever be a fraction or decimal?
5. How can you check if a point lies on the line given by a slope-intercept equation?

Tip: If you know the slope and one point on the line, you can also use the point-slope form to find the equation before converting it to slope-intercept form.