Explanation:
1a) The rate of change is the slope of the segment.
From A to B:
m = (4 mi − 0 mi) / (1 hr − 0 hr)
m = 4 mi/hr
From G to H:
m = (0 mi − 5 mi) / (10 hr − 8 hr)
m = -2.5 mi/hr
1b) From A to B, the distance is increasing, so the hiker is moving away from his home.
1c) The hiker was gone from home for 10 hours.
1d) The distance the hiker hikes is:
d = 4 mi + 2 mi + 0 mi + 2 mi + 1 mi + 0 mi + 5 mi
d = 14 mi
2a) As you found, the equation of the linear regression line is:
y = -0.005x + 47.78
2b) If the weight is 3500 lb, the expected fuel mileage is:
y = -0.005(3500) + 47.78
y = 30.28
2c) You can use Excel or a graphing calculator to find the correlation coefficient r², or you can calculate r manually:
r = ∑[(x − μₓ)(y − μᵧ)] / (sₓ sᵧ (n − 1))
where x is the weight, y is the mileage, μₓ is the average weight, μᵧ is the average mileage, sₓ is the standard deviation of the weights, sᵧ is the standard deviation of the mileages, and n is the number of data points.
μₓ = 3390, sₓ = 30.3
μᵧ = 842, sᵧ = 4.90
n = 9
r = (-29200) / (30.3 × 4.90 × (9 − 1))
r = -0.8848
r² = 0.7829