Question

card 4: the scatter plot shows the number of meals eaten at home and the number of dollars spent on fast food each week for students at lakeview high school. rasheeda says the data can be modeled by $y = .7x + 175$. raymond says the data can be modeled by $y = -7x + 140$.

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot shows that as the number of meals at home (\(x\)) increases, the dollars spent on fast food (\(y\)) decreases. So the slope of the line of best fit should be negative.

Step2: Check the slopes of the two equations

Rasheeda's equation: \(y = 0.7x + 175\) has a positive slope (\(0.7\)), which would imply a positive relationship (more home meals, more fast food spending), contradicting the scatter plot.
Raymond's equation: \(y=- 7x + 140\) has a negative slope (\(-7\)), which matches the negative trend (more home meals, less fast food spending) seen in the scatter plot.

Answer:

Raymond's model (\(y = -7x + 140\)) is correct because the scatter plot shows a negative correlation (as \(x\) increases, \(y\) decreases), and his equation has a negative slope, while Rasheeda's has a positive slope (contradicting the trend).