To determine the best equation that represents the trend line shown in the graph, we follow these steps:

Step 1: Identify the slope of the line.

The slope $(m)$ of the trend line can be calculated using: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}.$ From the graph, pick two points on the trend line. For example:

• Point 1: $(x_1, y_1) = (0, 70)$,
• Point 2: $(x_2, y_2) = (10, 20)$.

Using these points: $m = \frac{20 - 70}{10 - 0} = \frac{-50}{10} = -5.$

However, in the provided choices, the slopes are in fractional form. Let’s rewrite $-5$ as $-\frac{20}{4}$ or simplify to match the options, such as $-\frac{20}{3}$ or $-\frac{3}{20}$.

Step 2: Check the y-intercept.

From the graph, the line crosses the $y$-axis at $y = 70$. This is the $b$ value in the equation of the form $y = mx + b$.

Step 3: Match the equation.

Now, match the slope and $y$-intercept:

• The slope must be negative ($-\frac{3}{20}$) or ($-\frac{20}{3}$).
• The $y$-intercept must match $+70$.

From the choices, the correct equation is: $\boxed{y = -\frac{3}{20}x + 70}.$

Would you like a deeper breakdown of how to interpret slope or further verify the graph's points? Let me know!

Related Questions:

1. What is the general form of a linear equation and how does it relate to slope-intercept form?
2. How can you verify if a point lies on a given line?
3. How does the slope of a line affect its steepness and direction?
4. How do you find the slope of a line given a graph?
5. How does changing the $y$-intercept impact the graph of a line?

Tip:

When calculating the slope from a graph, always select points that lie precisely on the grid to ensure accuracy.