Question

summarizes why kyle is incorrect?

kyles equation has a negative y-intercept, but the scatterplot shows a point on the y-axis with a positive y-value.
kyles equation has a negative y-intercept, but the scatterplot shows a positive correlation.
kyles equation has a negative slope, but the scatterplot shows a point on the y-axis with a positive y-value.

Explanation:

Analyze the scatter plot data points

The scatter plot contains several points:

• On the \(y\)-axis (\(x = 0\)), there is a point at \((0, 1)\), which is a positive \(y\)-value.
• The overall trend of the data points goes from the bottom-left to the top-right, indicating a positive correlation (positive slope).

Evaluate the given options

• Option 1 states: "Kyle's equation has a negative \(y\)-intercept, but the scatterplot shows a point on the \(y\)-axis with a positive \(y\)-value." This directly and correctly identifies the contradiction between a negative \(y\)-intercept in Kyle's proposed equation and the actual data point on the \(y\)-axis.
• Option 2 states: "Kyle's equation has a negative \(y\)-intercept, but the scatterplot shows a positive correlation." While the scatterplot does show a positive correlation, the presence of a negative \(y\)-intercept does not inherently contradict a positive correlation (a line can have a positive slope and a negative \(y\)-intercept).
• Option 3 states: "Kyle's equation has a negative slope, but the scatterplot shows a point on the \(y\)-axis with a positive \(y\)-value." A negative slope does not contradict having a positive \(y\)-intercept.

Answer:

• (A) Kyle's equation has a negative y-intercept, but the scatterplot shows a point on the y-axis with a positive y-value. (Correct answer)
• (B) Kyle's equation has a negative y-intercept, but the scatterplot shows a positive correlation.
• (C) Kyle's equation has a negative slope, but the scatterplot shows a point on the y-axis with a positive y-value.