Question

The graph shows the tip amount that 14 different customers left, based on the their bill. A trend line has been drawn for the data. The equation for the line is: y = 0.14x + 2.5. Which BEST interprets the slope of the linear model? .

A) A $1 increase in the bill is associated with a $2.50 increase in tip amount.
B) A $2.50 increase in the bill is associated with a $1 increase in tip amount.
C) A $0.14 increase in the bill is associated with a $1 increase in tip amount.
D) A $1 increase in the bill is associated with a $0.14 increase in tip amount.

Answer 1

D) A $1 increase in the bill is associated with a $0.14 increase in tip amount.

Explanation:

Slope is 0.14

= change in tip/change in bill

When change in bill is $1, change in tip is $0.14

Answer 2

The correct interpretation of the slope in the equation y = 0.14x + 2.5 is: C) A $0.14 increase in the bill is associated with a $1 increase in tip amount. The slope (0.14) represents the rate of change, indicating that for each dollar increase in the bill x, the tip amount y increases by $0.14.

The linear model's equation y = 0.14x + 2.5 signifies that for each dollar increase in the bill x, the tip amount y rises by $0.14. The slope, 0.14, represents the rate of change in the tip amount concerning the bill.

This implies that a $1 increase in the bill corresponds to a $0.14 increase in the tip. Option C, "A $0.14 increase in the bill is associated with a $1 increase in tip amount," accurately captures this relationship.

The slope provides insights into the proportional change between the bill and tip, highlighting the linear association in the data.