To determine the equation of the line $l$, we need to follow these steps:

1. Find the slope:

The slope $m$ is calculated as: $m = \frac{\text{rise}}{\text{run}}$ From the graph:

• The line goes down from $y = 8$ to $y = 0$ as $x$ increases from $0$ to $6$.
• Rise $= -8$ (the vertical drop),
• Run $= 6$ (horizontal movement).

$m = \frac{-8}{6} = -\frac{4}{3}.$

2. Use the slope-intercept form:

The slope-intercept form of a line is: $y = mx + b$ where:

• $m$ is the slope,
• $b$ is the y-intercept.

From the graph, the y-intercept is $b = 8$. Substituting: $y = -\frac{4}{3}x + 8.$

3. Match the correct answer:

The correct option is B: $y = -\frac{4}{3}x + 8$.

Let me know if you want further clarifications!

5 Related Questions:

1. What is the slope of a horizontal line?
2. How do you calculate the slope of a line from two points?
3. What is the general equation of a straight line?
4. How do negative slopes affect the direction of a line?
5. What happens when the slope of a line is zero?

Tip:

Always verify both the slope and the y-intercept when identifying the equation of a line.