Here are the answers to the questions provided:
Question 14
Troy burns four calories per minute while walking his dog. The equation representing this proportional relationship is:
- Answer: y = 4x
Question 15
Given the values:
Hours: 2, 3, 4, 5
Temp: 60, 63, 70, 73
To check if it is proportional, calculate the differences:
- From 2 hours (60) to 3 hours (63) → increase of 3
- From 3 hours (63) to 4 hours (70) → increase of 7
- From 4 hours (70) to 5 hours (73) → increase of 3
Since the increases are not consistent, it is non-proportional.
- Answer: Non-proportional
Question 16
Given the values:
x: -9, -8, -7, -6
y: 13.5, 12, 10.5, 9
Check the ratios (y/x):
- -9: 13.5/-9 = -1.5
- -8: 12/-8 = -1.5
- -7: 10.5/-7 = -1.5
- -6: 9/-6 = -1.5
Each ratio is the same. Therefore, it is proportional.
- Answer: Proportional
Question 17
Given the values:
pictures: 40, 60, 80, 100
album pages: 10, 15, 20, 25
Compute the ratios:
- 40 pictures: 10 pages → 10/40 = 1/4
- 60 pictures: 15 pages → 15/60 = 1/4
- 80 pictures: 20 pages → 20/80 = 1/4
- 100 pictures: 25 pages → 25/100 = 1/4
All ratios are the same, so this is proportional with k-value 1/4 (or directly the proportion):
- Answer: Proportional; k = 1/4
Question 18
Gas costs $2.50 per gallon. The equation is:
- Answer: y = 2.50x
Question 19
To find the slope (m) between the points (12, 7) and (5, 9):
m = (y2 - y1) / (x2 - x1)
m = (9 - 7) / (5 - 12) = 2 / -7 = -2/7
- Answer: Slope = -2/7
Question 20
Given the table:
x: -9, -3, 0, 9
y: -5, -3, -2, 1
Calculate the slope using two points, e.g., (-9, -5) and (9, 1): m = (1 - (-5)) / (9 - (-9)) = (6) / (18) = 1/3
- Answer: Slope = 1/3
Question 21
Given the table:
x: -5, 0, 5, 10
y: 4, 1, -2, -5
Calculate the slope using two points, e.g., (0, 1) and (5, -2): m = (-2 - 1) / (5 - 0) = (-3) / (5) = -3/5
- Answer: Slope = -3/5
If you have any more questions or need further clarification, feel free to ask!
3 answers