Two-Variable Data: Models and Scatterplots Flashcards

A scatterplot shows data modeled by y = 3x² + 2. What is the predicted value of y when x = 4?

Answer: 50

Substitute x=4: y = 3(16)+2 = 48+2 = 50.

In a linear model y = mx + b, the slope m is negative. Which of the following is true as x increases by 1?

Answer: y decreases by |m|

A negative slope means each unit increase in x causes y to decrease by the magnitude of m.

A scatterplot shows points (1, 4), (2, 7), (3, 10), (4, 13). Which equation fits this data exactly?

Answer: y = 3x + 1

Check slope: (7−4)/(2−1) = 3; y-intercept from (1,4): 4 = 3(1)+b → b=1. Equation: y=3x+1.

The line of best fit for data on weekly exercise hours (x) and resting heart rate (y, bpm) is y = −2.5x + 80. What does the −2.5 represent?

Answer: For each additional hour of exercise per week, the resting heart rate decreases by 2.5 bpm on average.

The slope −2.5 represents the average change in y (resting heart rate) per unit increase in x (weekly exercise hours).

A best-fit line passes through (0, 5) and (10, 25). What is the equation of this line?

Answer: y = 2x + 5

Slope = (25−5)/(10−0) = 20/10 = 2; y-intercept = 5 (given). Equation: y = 2x+5.

A scatterplot of x and y has r = −0.88. Which of the following best describes the relationship?

Answer: Strong negative linear relationship

r = −0.88 is close to −1, indicating a strong negative linear correlation.

Data shows a pattern y ≈ 4 · 2^x. Which model best describes this data?

Answer: Exponential

The form y = a · b^x is an exponential model; here a = 4 and b = 2 (the growth factor).