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Write the equation of this line in slope-intercept form.

To find the equation of the line in slope-intercept form \( y = mx + b \), we need two key elements:

1. **The slope \( m \)** of the line.
2. **The y-intercept \( b \)** (the point where the line crosses the y-axis).

### Step 1: Find the Slope \( m \)
The slope is calculated using two points on the line. Looking at the graph, two clear points are:
- \( (2, -1) \)
- \( (-1, 2) \)

The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points:
\[
m = \frac{2 - (-1)}{-1 - 2} = \frac{2 + 1}{-3} = \frac{3}{-3} = -1
\]

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

### Step 2: Find the Y-Intercept \( b \)
From the graph, it's clear that the line crosses the y-axis at \( y = 1 \), so the y-intercept \( b = 1 \).

### Equation of the Line
Now that we have both the slope \( m = -1 \) and the y-intercept \( b = 1 \), the equation of the line is:
\[
y = -x + 1
\]

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

Would you like more details or have any questions about this?

### 5 Related Questions:
1. How do you calculate the slope if the points are not easily visible?
2. Can you find the equation of a line if only the slope and one point are known?
3. What is the significance of the y-intercept in real-life scenarios?
4. How do parallel and perpendicular lines relate to slope?
5. Can the slope of a line ever be zero or undefined?

### Tip:
When identifying points on a graph, try to pick points where the line crosses grid intersections for more accuracy in slope calculations.

Learn how to find the equation of a line in slope-intercept form based on a graph. This tutorial demonstrates how to calculate the slope and y-intercept from two points on the line and create the equation y = -x + 1. Suitable for Grades 8-10.

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