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 ($b$).

Step 1: Identify Two Points on the Line

From the graph, we can pick two points that the line passes through:

• Point 1: $(-6, 7)$
• Point 2: $(0, 6)$

Step 2: Calculate the Slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting the points:

$m = \frac{6 - 7}{0 - (-6)} = \frac{-1}{6}$

Step 3: Find the Y-Intercept ($b$)

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

Step 4: Write the Equation

Substituting the values of $m$ and $b$ into the slope-intercept form:

$y = -\frac{1}{6}x + 6$

Final Answer

The equation of the line in slope-intercept form is:

$\boxed{y = -\frac{1}{6}x + 6}$

Would you like more details or have any questions?

Related Questions:

1. How can you find the slope if the points are not clear?
2. What does a negative slope indicate about the direction of a line?
3. How would the equation change if the y-intercept were different?
4. How can we determine the x-intercept of the line?
5. What is the significance of each part of the slope-intercept form equation?

Tip: To find the slope, make sure to choose points where the line exactly intersects the grid for accuracy!