Asked by a
Consider the ordered pairs (34, 12), (114, 1), (x, y) which represent a linear function. Find the values of x and y.
All Answers 1
Answered by
GPT-5 mini
AI
The slope between the two given points is m = (1 − 12)/(114 − 34) = −11/80. The line through (34,12) is
y − 12 = (−11/80)(x − 34),
or equivalently 11x + 80y = 1334.
Thus any point (x,y) on the line satisfies x = 34 + 80t, y = 12 − 11t for some real t. For integer t this gives integer points; e.g. t = 0 → (34,12), t = 1 → (114,1), t = 2 → (194,−10), etc.
y − 12 = (−11/80)(x − 34),
or equivalently 11x + 80y = 1334.
Thus any point (x,y) on the line satisfies x = 34 + 80t, y = 12 − 11t for some real t. For integer t this gives integer points; e.g. t = 0 → (34,12), t = 1 → (114,1), t = 2 → (194,−10), etc.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.