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

Step 1: Identify the y-intercept

The y-intercept is where the line crosses the y-axis. From the graph, it crosses at $(0, 6)$, so: $b = 6$

Step 2: Calculate the Slope

The slope $m$ is determined by the "rise over run," or the change in y over the change in x between two points on the line.

Using the points $(0, 6)$ and $(2, 3)$:

• The change in y ($\Delta y$) from 6 to 3 is $3 - 6 = -3$.
• The change in x ($\Delta x$) from 0 to 2 is $2 - 0 = 2$.

So the slope $m$ is: $m = \frac{\Delta y}{\Delta x} = \frac{-3}{2}$

Step 3: Write the Equation

Using the slope-intercept form $y = mx + b$, we substitute $m = -\frac{3}{2}$ and $b = 6$: $y = -\frac{3}{2}x + 6$

Final Answer

The equation of the line is: $y = -\frac{3}{2}x + 6$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How can we find the slope if we know only two points on a line?
2. What is the significance of the y-intercept in a real-world context?
3. How would this equation change if the line had a positive slope?
4. What is the general form of a line's equation, and how does it relate to slope-intercept form?
5. How can we verify if a point lies on this line?

Tip: When finding the slope, always use points that are clearly marked on the grid to avoid errors.