Question

which linear equation best represents a trend line for the data in the scatter plot?
options:
y = -3x + 12
y = -\frac{1}{3}x + 15
y = -\frac{1}{3}x + 12
y = -\frac{1}{3}x - 12

Explanation:

Step1: Analyze the slope

The scatter plot shows a negative trend, so the slope is negative. Let's check the slope magnitude. The data points don't decrease very steeply, so a small negative slope (like \(-\frac{1}{3}\)) is more likely than a steep one (like \(-3\)). So we can eliminate \(y = -3x + 12\).

Step2: Analyze the y-intercept

When \(x = 0\), the y - value (y - intercept) of the trend line should be around 10 - 12 (from the scatter plot, when \(x = 0\), the points are around \(y = 10 - 12\)). Let's check the remaining options:

• For \(y=-\frac{1}{3}x + 15\), the y - intercept is 15, which is too high.
• For \(y =-\frac{1}{3}x+12\), the y - intercept is 12, which is reasonable.
• For \(y=-\frac{1}{3}x - 12\), the y - intercept is - 12, which is negative and doesn't match the scatter plot (the data is in the positive y - range when \(x = 0\)).

Answer:

\(y =-\frac{1}{3}x + 12\) (the option with this equation)