To find the equation of the line in slope-intercept form ($y = mx + b$), we need two key pieces of information:

1. The slope ($m$): This is the "rise over run," or the change in $y$ over the change in $x$.
2. The y-intercept ($b$): This is the point where the line crosses the $y$-axis.

Step 1: Find the slope $m$

Looking at the graph, the line passes through the points $(0, 16)$ and $(4, -4)$.

Using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(0, 16)$ and $(4, -4)$: $m = \frac{-4 - 16}{4 - 0} = \frac{-20}{4} = -5$ So, the slope $m = -5$.

Step 2: Find the y-intercept $b$

The y-intercept is the value of $y$ when $x = 0$. From the graph, we can see that the line crosses the $y$-axis at $16$. Therefore, $b = 16$.

Step 3: Write the equation

Now that we have the slope and the y-intercept, the equation of the line is: $y = -5x + 16$

This is the equation of the line in slope-intercept form.

Would you like any further details or explanations?

Here are 5 questions that expand on this concept:

1. How do you calculate the slope when given two points on a line?
2. What is the meaning of the slope and y-intercept in real-world problems?
3. How does the slope affect the direction of a line on a graph?
4. How would the equation change if the line had a positive slope?
5. Can you determine the equation of a vertical or horizontal line?

Tip: The steeper the line, the larger the absolute value of the slope!