The problem involves determining the equation of a line shown in the graph. Let’s analyze the components:

1. The line has a negative slope, indicating a decreasing relationship between $x$ and $y$.
2. The $y$-intercept (where $x = 0$) appears to be at $y = 16$.

Step 1: Determine the slope ($m$)

To calculate the slope ($m$), we use the formula: $m = \frac{\Delta y}{\Delta x}$ Looking at the graph:

• The first point is $(0, 16)$.
• Another clear point on the line is $(1, 12)$.

The change in $y$ ($\Delta y$) is: $\Delta y = 12 - 16 = -4$ The change in $x$ ($\Delta x$) is: $\Delta x = 1 - 0 = 1$

Thus, the slope is: $m = \frac{-4}{1} = -4$

Step 2: Write the equation

The general form of the line is: $y = mx + b$ Here:

• $m = -4$ (slope)
• $b = 16$ (y-intercept)

Substituting these values, the equation is: $y = -4x + 16$

The equation written in the box ("$y = -16$") is incorrect because it doesn't include the correct slope or intercept.

Would you like further clarification, or should I proceed with related questions to expand understanding? Here are 5 questions to deepen the concept:

1. How can the slope of a line be interpreted in real-world situations?
2. What happens to the equation of a line if the slope is 0?
3. How can you verify the equation of a line by substituting points from the graph?
4. How does the slope of a line affect its steepness and direction?
5. What is the difference between positive and negative slopes?

Tip: Always confirm the slope by checking at least two points to ensure accuracy.