A graph titled Monthly Sales and Advertising Costs has Advertising Costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. A line goes through points (6.4, 117) and (6.6, 120).

Question

The scatterplot and trend line show a positive correlation between advertising costs and sales.

Using the points (6.4, 117) and (6.6, 120), what is the slope of the trend line?
–15
–12
12
15

Answer 1

To find the slope of the trend line that passes through the points \((6.4, 117)\) and \((6.6, 120)\), we use the formula for the slope \(m\) of a line, which is defined as:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can assign the points as follows:

• \((x_1, y_1) = (6.4, 117)\)
• \((x_2, y_2) = (6.6, 120)\)

Now we can substitute the values into the formula:

\[ m = \frac{120 - 117}{6.6 - 6.4} = \frac{3}{0.2} = 15 \]

Thus, the slope of the trend line is 15.