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To find the equation of the line represented in the graph, we need to determine both the **slope** (denoted by \( m \)) and the **y-intercept** (denoted by \( b \)).

### Step 1: Identify two points on the line
From the graph, two points on the line are:

1. \( (2, 0) \)
2. \( (0, 2) \)

### Step 2: Calculate the slope \( m \)
The slope \( m \) of a line is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (x_1, y_1) = (2, 0) \) and \( (x_2, y_2) = (0, 2) \):
\[
m = \frac{2 - 0}{0 - 2} = \frac{2}{-2} = -1
\]
Thus, the slope of the line is \( m = -1 \).

### Step 3: Write the equation in slope-intercept form
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
We know the slope \( m = -1 \), and from the graph, the **y-intercept** is \( b = 2 \) (the point where the line crosses the y-axis).

Therefore, the equation of the line is:
\[
y = -x + 2
\]

Would you like more details on any part of this solution? Here are some related questions for further exploration:

1. How can you find the equation of a line given any two points?
2. What is the geometric significance of the slope of a line?
3. How do you derive the slope-intercept form from the standard form of a linear equation?
4. How do you interpret the y-intercept in real-world problems?
5. What are the different forms of linear equations?

**Tip:** Always check your calculations by substituting points from the graph back into the equation to verify correctness.

Escreva uma equação que represente a reta. Use números exatos.

Learn how to write the equation of a line with slope -1 and y-intercept 2. This detailed solution uses the slope-intercept form and includes the calculation of the slope from two points on the graph. Suitable for students in Grades 8-10.

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