write an equation that represents the line

To write the equation of the line shown in the graph, let's determine the slope (\(m\)) and the y-intercept (\(b\)) from the graph.

### 1. **Identifying the Slope (\(m\)):**
   - The slope (\(m\)) is the "rise over run," which means the change in \(y\) over the change in \(x\).
   - Let's pick two points on the line. From the graph, it looks like the line passes through the points \((0, 3)\) and \((3, 0)\).

   - The slope can be calculated using the formula:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1}
     \]
     Substituting the points \((0, 3)\) and \((3, 0)\):
     \[
     m = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1
     \]

### 2. **Identifying the Y-Intercept (\(b\)):**
   - The y-intercept (\(b\)) is the value of \(y\) where the line crosses the y-axis. From the graph, the line crosses the y-axis at \(y = 3\).
   - Therefore, \(b = 3\).

### 3. **Writing the Equation:**
   - The equation of the line in slope-intercept form is:
     \[
     y = mx + b
     \]
   - Substituting the values of \(m\) and \(b\) we found:
     \[
     y = -1x + 3 \quad \text{or simply} \quad y = -x + 3
     \]

So, the equation that represents the line is **\(y = -x + 3\)**.

Would you like more details or have any further questions?

Here are five related questions to expand on this topic:

1. How can you find the equation of a line if given two points?
2. What does it mean when a line has a slope of zero?
3. How do you interpret the slope and y-intercept in a real-world context?
4. What happens to the graph of the line if the y-intercept is negative?
5. How can you rewrite the equation \(y = -x + 3\) in standard form?

**Tip:** Remember, the slope tells you the steepness of the line, and the y-intercept tells you where the line crosses the y-axis.

Learn how to write the equation of a line using the slope-intercept form with a detailed step-by-step solution. This problem covers linear equations, slope calculation, and the interpretation of y-intercept. Suitable for students in Grades 7-9.

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