To solve this problem, let's first analyze the given image and identify the question and answer choices.

Analysis of the Image

The question in the image asks, "Which equation represents the dotted line?" There are four answer choices provided:

• A) $y = \frac{2}{3}x - 4$
• B) $y = -\frac{2}{3}x - 4$
• C) $y = \frac{3}{2}x - 4$
• D) $y = -\frac{3}{2}x - 4$

The graph shows a line that appears to cross the y-axis at -4 and has a negative slope.

Determine the Correct Equation

1. Identify the y-intercept (b): The line crosses the y-axis at $-4$. So, the y-intercept $b = -4$.

2. Determine the slope (m): The line has a negative slope. To find the slope, we can use the rise-over-run method:

   • The line goes down 3 units vertically (rise = -3) and goes right 2 units horizontally (run = 2).
   • Slope, $m = \frac{\text{rise}}{\text{run}} = \frac{-3}{2} = -\frac{3}{2}$.

3. Form the equation: Now, using the slope-intercept form of the line equation, $y = mx + b$, and substituting the slope $-\frac{3}{2}$ and y-intercept $-4$, the equation of the line is:

   $y = -\frac{3}{2}x - 4$

Conclusion

The correct answer is D) $y = -\frac{3}{2}x - 4$.

Would you like more details on this solution, or do you have any other questions?

Here are 5 related questions that might interest you:

1. How do you find the slope of a line from two given points?
2. What are the differences between positive and negative slopes?
3. How can you determine if a point lies on a given line?
4. What is the standard form of a linear equation, and how does it differ from the slope-intercept form?
5. How do you convert an equation from slope-intercept form to standard form?

Tip: Always identify the y-intercept and slope from the graph first, as they are crucial for determining the correct equation.