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The equation of a line in slope-intercept form is written as:

\[
y = mx + b
\]

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

### Step 1: Find the Slope (m)

To find the slope, we need two points on the line. From the graph, we can identify two points:
- Point 1: (-10, -7)
- Point 2: (10, 8)

The slope formula is:

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

Substituting the coordinates of the points:

\[
m = \frac{8 - (-7)}{10 - (-10)} = \frac{8 + 7}{10 + 10} = \frac{15}{20} = \frac{3}{4}
\]

So, the slope of the line is \( \frac{3}{4} \).

### Step 2: Find the y-intercept (b)

From the graph, we can see that the line crosses the y-axis at \( b = -5 \). Thus, the y-intercept is \( -5 \).

### Step 3: Write the Equation

Now that we have both the slope \( m = \frac{3}{4} \) and the y-intercept \( b = -5 \), the equation of the line is:

\[
y = \frac{3}{4}x - 5
\]

This is the fully simplified equation of the line in slope-intercept form.

Would you like more details or further clarification? Here are five related questions for exploration:

1. How do you find the equation of a line if you are given only the slope and one point?
2. What happens if the slope is negative? How would the graph change?
3. Can you derive the equation of a vertical line in slope-intercept form?
4. How can you determine if two lines are parallel or perpendicular from their equations?
5. What is the importance of the slope in determining the behavior of a line?

**Tip:** When calculating the slope, always simplify your result as much as possible to avoid errors in the final equation.

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

Learn how to derive the equation of a line in slope-intercept form from a graph. This example includes identifying two points on the line, calculating the slope using the slope formula, and determining the y-intercept. A step-by-step guide with solutions for students in Grades 8-10.

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