To determine the equation of the line from the graph, we need to follow these steps:

1. Identify two points on the line:

From the graph, the line passes through the following points:

• $(-5, -2)$
• $(-2, 1)$
• $(2, 3)$
• $(6, 5)$

2. Calculate the slope $m$:

The slope formula is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using two points, say $(-5, -2)$ and $(-2, 1)$:

$m = \frac{1 - (-2)}{-2 - (-5)} = \frac{1 + 2}{-2 + 5} = \frac{3}{3} = 1$ Thus, the slope $m = 1$.

3. Use the slope-intercept form:

The general equation of a line in slope-intercept form is: $y = mx + b$ Substitute $m = 1$ into the equation: $y = x + b$

4. Find the y-intercept $b$:

To find $b$, use any of the points on the line. Let's use the point $(2, 3)$: $3 = 1(2) + b \implies 3 = 2 + b \implies b = 1$

5. Write the final equation:

Thus, the equation of the line is: $y = x + 1$

Would you like further details or clarification on any part of the process?

Here are 5 related questions you could explore:

1. How would the equation change if the slope were negative?
2. What happens if the line passes through the origin?
3. Can you determine the equation of a line parallel to this one?
4. How do you calculate the equation if only one point and the slope are given?
5. What is the significance of the y-intercept in the context of real-world applications?

Tip: When identifying the slope from a graph, it's often easiest to choose two points where the line crosses the grid precisely to avoid estimation errors.