To find the equation of the line in slope-intercept form $y = mx + b$, we need to determine the slope $m$ and the y-intercept $b$ of the line.

Step 1: Determine the Slope (m)

To calculate the slope, we can pick two points on the line and use the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ From observing the graph:

1. One point on the line is $(0, -6)$, which is also the y-intercept.
2. Another point on the line is $(6, 6)$.

Calculating the slope: $m = \frac{6 - (-6)}{6 - 0} = \frac{12}{6} = 2$

Step 2: Determine the Y-intercept (b)

Since the line crosses the y-axis at $(0, -6)$, the y-intercept $b = -6$.

Step 3: Write the Equation

With $m = 2$ and $b = -6$, the equation of the line is: $y = 2x - 6$

Would you like further details or have any questions?

Here are some related questions for practice:

1. How would you find the equation of a line passing through two different points?
2. How does changing the slope affect the angle of a line on a graph?
3. How would the equation change if the line had a negative slope?
4. What is the significance of the y-intercept in real-world applications?
5. How would you convert a line equation from standard form to slope-intercept form?

Tip: In a linear equation $y = mx + b$, the slope $m$ describes the steepness, while $b$ represents where the line crosses the y-axis.