Question

for the data given below, answer parts (a) through (d)

x	-19	-16	-14	-13	-9
y	102	122	120	132	142

(c) use a graphing utility to find the line of best fit.
which of the following is the equation of the line of best fit?
a. $y = -3.9613x + 178.4307$
b. $y = 3.9613x + 178.4307$
c. $y = -3.8613x + 178.4307$
d. $y = 3.8613x + 178.4307$

Explanation:

Step1: Analyze the trend of x and y

As x increases (from -19 to -9), y also increases (from 102 to 142). So the slope of the line of best fit should be positive. This eliminates options A and C (which have negative slopes).

Step2: Calculate the slope (approximate)

We can use two points, e.g., \((x_1,y_1)=(-19,102)\) and \((x_2,y_2)=(-9,142)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{142 - 102}{-9 - (-19)}=\frac{40}{10} = 4\). Now check the slopes of options B and D. Option B has a slope of 3.9613 (close to 4), option D has 3.8613. 3.9613 is closer to 4.

Answer:

B. \( y = 3.9613x + 178.4307 \)