Looking at the graph, we need to identify which equation represents the line shown.

Step-by-step approach:

1. Find the slope (m):

   • From the graph, we can see that the line passes through the points $(0, 4)$ and $(4, 0)$.
   • The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 4)$ and $(4, 0)$: $m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1$

2. Find the y-intercept (b):

   • The y-intercept is the point where the line crosses the y-axis, which happens at $(0, 4)$. So, the y-intercept is 4.

3. Form the equation:

   • Using the slope-intercept form $y = mx + b$, where $m = -1$ and $b = 4$: $y = -x + 4 \quad \text{or} \quad y = 4 - x$

4. Choose the correct equation:

   • Among the options, the correct equation is $y = 4 - x$.

Answer:

The correct option is the third one: $y = 4 - x$.

Would you like further details or have any other questions?

Here are five questions related to this topic:

1. How can you identify the slope of a line given two points?
2. What does the y-intercept tell you about a graph?
3. How would the equation change if the line had a positive slope?
4. How do you convert a linear equation from slope-intercept form to standard form?
5. What other methods can be used to find the equation of a line given a graph?

Tip: When reading a graph, always identify the points where the line intersects the axes first. These points make finding the slope and equation easier.