Question

the scatter plot shows the number of text messages sent (x) and text messages received (y) by 10 students in a half hour. which equation could be used to find the best estimate for the number of text messages received based on the number of text messages sent? a y = x b y = 2x c y = x + 2 d y = 2x + 1

Explanation:

Step1: Analyze the trend of the scatter - plot

We observe the relationship between \(x\) (texts sent) and \(y\) (texts received). We can check each option by substituting some \(x\) values.

Step2: Check Option A (\(y = x\))

If \(x = 2\), then \(y=2\). But from the scatter - plot, when \(x = 2\), \(y\approx4\). So Option A is incorrect.

Step3: Check Option B (\(y = 2x\))

If \(x = 2\), then \(y = 4\); if \(x=6\), then \(y = 12\). But from the scatter - plot, when \(x = 6\), \(y\approx6\). So Option B is incorrect.

Step4: Check Option C (\(y=x + 2\))

If \(x=2\), then \(y=4\); if \(x = 6\), then \(y=8\). But from the scatter - plot, when \(x = 6\), \(y\approx6\). So Option C is incorrect.

Step5: Check Option D (\(y=\frac{1}{2}x+1\))

If \(x = 2\), \(y=\frac{1}{2}\times2+1=2 + 1=3\approx4\) (considering approximation in scatter - plot trend). If \(x=12\), \(y=\frac{1}{2}\times12 + 1=6 + 1=7\approx8\) (approximate match with the general trend of the scatter - plot points).

Answer:

D. \(y=\frac{1}{2}x + 1\)