To find the equation of the line in the form $y = mx + c$ (where $m$ is the slope and $c$ is the y-intercept), let's extract the necessary information from the graph.

Step 1: Identify two points on the line

From the graph, we can select two clear points that the line passes through:

• Point $A$ at $(0, 4)$
• Point $B$ at $(4, 0)$

Step 2: Calculate the slope $m$

The slope $m$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For points $A(0, 4)$ and $B(4, 0)$:

$m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1$

So, the slope $m = -1$.

Step 3: Find the y-intercept $c$

The y-intercept is the value of $y$ when $x = 0$. From the graph, we can see that when $x = 0$, $y = 4$. Therefore, $c = 4$.

Step 4: Write the equation

Now that we have the slope $m = -1$ and the y-intercept $c = 4$, the equation of the line is:

$y = -x + 4$

Would you like more details or have any questions on this?

Here are some questions to extend this:

1. How do you calculate the slope if the line is vertical or horizontal?
2. What happens to the equation of a line when the slope is 0?
3. Can you rewrite the equation in general form $Ax + By + C = 0$?
4. How do you interpret the slope and y-intercept in real-world situations?
5. What effect does changing the slope $m$ have on the steepness of the line?

Tip: The slope of a line indicates its steepness and direction. A negative slope means the line is sloping downwards as you move from left to right.