Final answer:
To find the values of m for each value of n from the equation 8n = -3m + 1, we isolate m and then substitute the given values of n (-2, 2, 4) to obtain the corresponding values of m. The correct answer is (a) m = -8/3n + 1/3, with m values being -5 2/3, -5, and -10 1/3 respectively.
Step-by-step explanation:
To find the value of m for each given value of n, we start with the equation 8n = -3m + 1. To solve for m, we need to rearrange the equation to isolate m on one side:
- Add 3m to both sides: 3m + 8n = 1
- Subtract 8n from both sides: 3m = 1 - 8n
- Divide both sides by 3 to solve for m: m = (1 - 8n) / 3
Now we substitute the given values of n into this equation and calculate m:
- For n = -2: m = (1 - 8(-2)) / 3 = (1 + 16) / 3 = 17/3 = 5 2/3
- For n = 2: m = (1 - 8(2)) / 3 = (1 - 16) / 3 = -15/3 = -5
- For n = 4: m = (1 - 8(4)) / 3 = (1 - 32) / 3 = -31/3 = -10 1/3
Therefore, the correct answer that matches with these calculations is (a) m = -8/3n + 1/3, with the values -5 2/3, -5, and -10 1/3 for n = -2, 2, and 4 respectively.