To solve the problem, we will analyze the graph and identify the slope and $y$-intercept of the line. Then, we'll write the equation in slope-intercept form, which is given by:

$y = mx + b$

where $m$ is the slope, and $b$ is the $y$-intercept.

Step 1: Determine the slope ($m$)

The slope is calculated as:

$m = \frac{\text{rise}}{\text{run}}$

From the graph, two points are clearly identified:

• Point $(0, 16)$
• Point $(12, 4)$

The "rise" is the change in $y$-values: $\text{rise} = 16 - 4 = 12$

The "run" is the change in $x$-values: $\text{run} = 0 - 12 = -12$

Thus, the slope is: $m = \frac{\text{rise}}{\text{run}} = \frac{12}{-12} = -1$

Step 2: Identify the $y$-intercept ($b$)

From the graph, the $y$-intercept is the point where the line crosses the $y$-axis. This is clearly $(0, 16)$. Hence: $b = 16$

Step 3: Write the equation of the line

Substituting $m = -1$ and $b = 16$ into the slope-intercept form $y = mx + b$: $y = -x + 16$

Final Answer:

The slope-intercept form of the equation is: $\boxed{y = -x + 16}$

Would you like me to break down any of these steps further or verify additional points?

Related Questions:

1. How do you calculate the slope of a line given two points?
2. What is the significance of the $y$-intercept in the slope-intercept form of a line?
3. How does a negative slope affect the direction of a line?
4. How would the equation change if the slope were positive instead of negative?
5. What are the other forms of the equation of a line besides slope-intercept form?

Tip:

Always verify the slope calculation by ensuring consistent directions for "rise" (change in $y$) and "run" (change in $x$).