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Which equation represents the graphed lin

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).

Learn how to identify the equation of a graphed line with a slope of -1 and a y-intercept of 4. This problem covers key algebraic concepts, including linear equations, slope calculation, and y-intercept determination. Suitable for students in Grades 7-9.

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