To determine the equation of the line in slope-intercept form ($y = mx + b$), we need two key components:

1. Slope $(m)$
2. Y-intercept $(b)$

Step 1: Find the slope $m$

The slope $m$ is given by the formula: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$ Looking at the graph:

• The line passes through two easily identifiable points: $(-6, 7)$ and $(0, 3)$.

Using these points: $m = \frac{3 - 7}{0 - (-6)} = \frac{-4}{6} = -\frac{2}{3}$ So, the slope $m = -\frac{2}{3}$.

Step 2: Find the y-intercept $b$

From the graph, the line crosses the y-axis at $y = 3$, so the y-intercept is $b = 3$.

Step 3: Write the equation

Now that we have both the slope and the y-intercept, we can write the equation in slope-intercept form: $y = -\frac{2}{3}x + 3$

Final Answer:

$y = -\frac{2}{3}x + 3$

Would you like further clarification on any part of this process?

Here are some related questions:

1. What does the slope of a line represent geometrically?
2. How would the equation change if the line had a positive slope?
3. What is the equation of a line with the same slope but a different y-intercept?
4. How can you find the slope if the line is given in standard form (Ax + By = C)?
5. Can the slope-intercept form be derived from two points not on the axes?

Tip: Always check for points where the line crosses the grid for easy identification of coordinates!