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

1. The slope (m): The slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
2. The y-intercept (b): This is the point where the line crosses the y-axis.

Step 1: Determine the slope (m)

From the graph, let's choose two points on the line:

• The line passes through $(-6, 6)$ and $(0, 2)$.

Using the slope formula: $m = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values from the points $(-6, 6)$ and $(0, 2)$: $m = \frac{2 - 6}{0 - (-6)} = \frac{-4}{6} = -\frac{2}{3}$ So, the slope $m = -\frac{2}{3}$.

Step 2: Determine the y-intercept (b)

The y-intercept is the point where the line crosses the y-axis, which from the graph is at $(0, 2)$. Therefore, $b = 2$.

Final Equation:

The equation of the line in slope-intercept form is: $y = -\frac{2}{3}x + 2$

Would you like more details or have any questions?

Here are 5 related questions to extend your learning:

1. What is the general form of a linear equation, and how is it related to the slope-intercept form?
2. How can you find the slope if only the graph of the line is given?
3. How do changes in the slope affect the steepness of a line on a graph?
4. How can you convert the slope-intercept form to standard form $Ax + By = C$?
5. What is the significance of the y-intercept in real-world scenarios?

Tip: Always check two points on the line carefully to ensure an accurate calculation of the slope.