The graph shows a red line, and we are tasked with identifying its equation.

Step 1: Identify two points on the line

From the graph:

1. The first point is $(-1, -3)$.
2. The second point is $(1, -1)$.

Step 2: Calculate the slope

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{-1 - (-3)}{1 - (-1)} = \frac{-1 + 3}{1 + 1} = \frac{2}{2} = 1$

Step 3: Write the equation in slope-intercept form

The general slope-intercept form of a line is: $y = mx + b$ We know $m = 1$, so: $y = x + b$

Step 4: Solve for $b$ (the y-intercept)

Substitute one of the points, say $(1, -1)$, into the equation $y = x + b$: $-1 = 1 + b$ $b = -1 - 1 = -2$

Final Equation

The equation of the line is: $y = x - 2$

Would you like further clarification or an exploration of related topics? Here are five follow-up questions:

1. How do you determine the slope when the line is vertical or horizontal?
2. What happens to the equation if the y-intercept is zero?
3. Can you convert this line equation to standard form $Ax + By = C$?
4. How do you calculate the distance between two points on a graph?
5. How do parallel and perpendicular slopes relate to this equation?

Tip: Always verify your line equation by substituting at least two points from the graph into the equation to ensure it fits perfectly!