The given image shows a line on a graph, and you are asked to determine the equation of the line in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Let's determine the slope (m):

The line crosses two clear points on the grid:

• Point 1: $(-4, -4)$
• Point 2: $(4, 4)$

To calculate the slope $m$, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points:

$m = \frac{4 - (-4)}{4 - (-4)} = \frac{8}{8} = 1$

Determining the y-intercept (b):

From the graph, the line crosses the y-axis at $b = 0$.

Final equation:

The equation of the line is:

$y = 1x + 0$

Simplified, it is:

$y = x$

Would you like further clarification, or do you have more questions?

Here are five related questions to deepen understanding:

1. What happens to the slope if the line becomes steeper?
2. How do we calculate the slope if the line is horizontal?
3. What would the equation look like if the y-intercept was $b = 2$?
4. How does the equation change if the line passes through the origin?
5. What is the significance of the slope being positive or negative?

Tip: A line with a slope of 1 rises one unit for every unit it moves to the right.