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To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.

The **slope-intercept form** of a line is given by:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

### 1. Identify two points on the line:
From the graph, we can identify two points:
- \( (-6, 5) \)
- \( (6, -7) \)

### 2. Calculate the slope \( m \):
The slope \( m \) is the change in \( y \) divided by the change in \( x \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (-6, 5) \) and \( (6, -7) \):

\[
m = \frac{-7 - 5}{6 - (-6)} = \frac{-12}{12} = -1
\]

So, the slope \( m \) is \( -1 \).

### 3. Determine the y-intercept \( b \):
To find \( b \), we can use one of the points and substitute the values of \( x \), \( y \), and \( m \) into the slope-intercept form \( y = mx + b \).

Using the point \( (-6, 5) \):

\[
5 = (-1)(-6) + b
\]
\[
5 = 6 + b
\]
\[
b = 5 - 6 = -1
\]

So, the y-intercept \( b \) is \( -1 \).

### 4. Write the equation:
Now that we know \( m = -1 \) and \( b = -1 \), the equation of the line is:

\[
y = -x - 1
\]

Would you like any further details or have any questions about this solution?

### Related Questions:
1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How do you convert a line equation from slope-intercept form to standard form?
4. What does the slope of a line represent in real-world situations?
5. How can we verify the correctness of the slope using another method?

### Tip:
When calculating the slope, always double-check that you've correctly identified the change in \( y \) and \( x \) (rise over run).

Write the equation of the line in fully simplified slope-intercept form based on the graph.

Learn how to find the equation of a line in slope-intercept form using two points on a graph. This example covers key algebraic concepts, including the slope formula and y-intercept calculation. Ideal for Grades 8-10 students.

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