Question

use a graphing calculator to find an equation of the line of best fit for the data.
4.

x	-12	-9	-6	-3	0	3	6	9	12
y	-27	-15	-2	6	21	30	42	58	67

q. $y = -3.9x - 20$ r. $y = 3.9x - 20$ s. $y = 3.9x + 20$
5.

x	-4	-3	-2	-1	0	1	2	3	4
y	15	12	5	3	-5	-10	-13	-20	-23

a. $y = 4.95x + 4$ b. $y = -4.95x - 4$ c. $y = -4.95x + 4$

Explanation:

for Question 4:

Step 1: Analyze the slope sign

As \( x \) increases (from -12 to 12), \( y \) also increases (from -27 to 67), so the slope should be positive. Eliminate option Q (negative slope).

Step 2: Test the y-intercept

When \( x = 0 \), from the data, \( y = 21 \). Let's check the y - intercept (when \( x = 0 \)) of options R and S. For option R: \( y=3.9(0)-20=-20\) (not 21). For option S: \( y = 3.9(0)+20 = 20\) (close to 21, considering approximation). So option S is correct.

for Question 5:

Step 1: Analyze the slope sign

As \( x \) increases (from -4 to 4), \( y \) decreases (from 15 to -23), so the slope should be negative. Eliminate option A (positive slope).

Step 2: Test the y - intercept

When \( x = 0 \), from the data, \( y=-5\). Let's check the y - intercept (when \( x = 0 \)) of options B and C. For option B: \( y=-4.95(0)-4=-4\) (close to -5). For option C: \( y=-4.95(0)+4 = 4\) (not close to -5). So option B is correct.

Answer:

1. S. \( y = 3.9x + 20 \)
2. B. \( y = -4.95x - 4 \)