Question

solving and writing about equations of trend lines
monthly sales & advertising costs
the scatterplot and trend line show a positive
correlation between advertising costs and sales.
which two points can be used to find the slope of the
trend line?
point 1:
point 2:
(6.5, 122)
(6.6, 120)
(6.7, 121)
(6.9, 123)

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We need two points \((x_1,y_1)\) and \((x_2,y_2)\) that lie on the trend - line.

Step2: Analyze the given points

Looking at the scatter - plot and trend - line:

• For the point \((6.5,122)\) and \((6.9,123)\):
• Here \(x_1 = 6.5,y_1=122,x_2 = 6.9,y_2 = 123\).
• These points are on the trend - line (as we can assume from the nature of trend - line selection for slope calculation where we pick two well - defined points on the line of best fit).
• For \((6.6,120)\): This point is not on the trend - line (since the trend - line shows a positive correlation and \(y\) should increase as \(x\) increases. If \(x = 6.6\), from the trend - line's upward - sloping nature, \(y\) should be higher than some adjacent values).
• For \((6.7,121)\): This point is not on the trend - line (the trend - line is a smooth line of best fit, and this point may be an out - lying data point relative to the trend - line for slope calculation).

Answer:

Point 1: \((6.5,122)\)
Point 2: \((6.9,123)\)