Final answer:
After simplifying the given equation y - 7 = 3(x - 12) to y = 3x - 29, it becomes apparent that none of the provided options A) 3x + y = 8, B) 3x + 4y = 12, C) 3x - y = 5, or D) 3x – 4y = 8 represent the same line as they each lead to different forms upon simplification.
Step-by-step explanation:
The equation of a line given as y – 7 = 3(x – 12) can be simplified to find an equivalent equation. We will distribute the 3 and move terms around to match one of the given options.
- y - 7 = 3x - 36
- y = 3x - 36 + 7
- y = 3x - 29
To find the equation that represents this same line, we look for the one that can be similarly arranged.
- A) 3x + y = 8 (3x - 8 = y, not in the same form)
B) 3x + 4y = 12 (not in the same form)
C) 3x - y = 5 (3x - 5 = y, not in the same form)
- D) 3x – 4y = 8 (3x - 8 = 4y -> y = 3x/4 - 2, not in the same form)
- Upon reviewing these options, we can conclude that none of these equations exactly represent the original equation
- y = 3x - 29
- .