To determine the equation that represents the graphed line, we can follow these steps:

1. Identify the Slope (m)

The slope of a line is calculated by using the formula:

$m = \frac{\text{rise}}{\text{run}}$

Looking at the graph:

• The line passes through the points $(0, 4)$ and $(4, 0)$.
• The "rise" (change in $y$) is $-4$ (from $4$ to $0$).
• The "run" (change in $x$) is $4$ (from $0$ to $4$).

Thus, the slope $m$ is:

$m = \frac{-4}{4} = -1$

2. Determine the y-intercept (b)

The $y$-intercept is the point where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $y = 4$. Therefore, $b = 4$.

3. Write the Equation

The general form of a linear equation is:

$y = mx + b$

Substituting the values of $m$ and $b$:

$y = -1x + 4$

This simplifies to:

$y = -x + 4$

Conclusion

The equation that represents the graphed line is:

$\boxed{y = -x + 4}$

Would you like more details or have any questions?

Related Questions:

1. What is the slope of a line parallel to the graphed line?
2. How would the equation change if the line was shifted up by 2 units?
3. Can you find the equation of a line perpendicular to the graphed line?
4. What is the x-intercept of the line in the graph?
5. How would you graph the line $y = 2x - 3$ on the same grid?

Tip:

Remember, the slope indicates the steepness of the line and the direction in which it moves (upwards or downwards).