To write the equation of the line in slope-intercept form $y = mx + b$, we need two key pieces of information from the graph:

1. Slope (m): The slope is the change in $y$ divided by the change in $x$, often referred to as "rise over run."
2. Y-intercept (b): This is the point where the line crosses the $y$-axis.

Step 1: Find the slope (m)

Looking at the graph, we can choose two points that the line passes through. These points are:

• $(-4, -2)$
• $(4, 6)$

Now, calculate the slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-2)}{4 - (-4)} = \frac{6 + 2}{4 + 4} = \frac{8}{8} = 1$ So, the slope $m = 1$.

Step 2: Find the y-intercept (b)

The line crosses the $y$-axis at $y = 2$. Therefore, the $y$-intercept $b = 2$.

Step 3: Write the equation

Now that we know the slope $m = 1$ and the y-intercept $b = 2$, we can write the equation in slope-intercept form: $y = 1x + 2$ or simply: $y = x + 2$

Would you like more details or have any questions?

Here are 5 related questions to further explore:

1. How would the equation change if the slope were negative?
2. What is the equation of a horizontal line passing through $y = 2$?
3. How do we calculate the slope if given only two points on the line?
4. Can we write the equation of a vertical line in slope-intercept form?
5. What are the key differences between slope-intercept form and point-slope form?

Tip: When graphing a line, always choose points that fall on the intersections of the grid to calculate the slope more accurately!