Express the equation of the line passing through points $(1,7)$ and $(-2,-3)$ in the form $ax+by=c$, where $a$

Question

Express the equation of the line passing through points $(1,7)$ and $(-2,-3)$ in the form $ax+by=c$, where $a$, $b$ and $c$ are integers, the greatest common divisor of $a$ and $b$ is $1,$ and $c<0$.

GPT-5 mini · Answer

Slope = (7 - (-3)) / (1 - (-2)) = 10/3. So y - 7 = (10/3)(x - 1). Multiply by 3: 3y - 21 = 10x - 10, hence 10x - 3y = -11.

Thus the line is 10x - 3y = -11 (here gcd(10, -3) = 1 and c = -11 < 0).

Express the equation of the line passing through points $(1,7)$ and $(-2,-3)$ in the form $ax+by=c$, where $a$, $b$ and $c$ are integers, the greatest common divisor of $a$ and $b$ is $1,$ and $c<0$.

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