To find the equation of the line in the given graph, we need to determine the slope ($m$) and the y-intercept ($b$) and express the line in the slope-intercept form:

$y = mx + b$

Step 1: Identify two points on the line

From the graph:

1. Point 1: $(-4, -2)$
2. Point 2: $(4, 6)$

Step 2: Calculate the slope

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates: $m = \frac{6 - (-2)}{4 - (-4)} = \frac{6 + 2}{4 + 4} = \frac{8}{8} = 1$

Thus, the slope $m = 1$.

Step 3: Find the y-intercept

The y-intercept ($b$) is the value of $y$ when $x = 0$. Observing the graph, when $x = 0$, $y = 2$.

So, $b = 2$.

Final Equation:

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

Let me know if you'd like further clarifications or additional steps! Here are 5 related questions for further exploration:

1. How do you determine the slope when the points are not given explicitly on the graph?
2. What is the relationship between the slope and the angle of a line?
3. How do parallel lines compare in terms of their slopes?
4. How can the equation of a line be expressed in standard form?
5. What happens to the equation if the y-intercept changes?

Tip: Always double-check the graph for the exact coordinates when calculating slope and intercepts.