Find the equation of the line perpendicular to y=13x that passes through (7,8)

Kayla Mcdowell
2022-10-12
Answered

Find the equation of the line perpendicular to y=13x that passes through (7,8)

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cdtortosadn

Answered 2022-10-13
Author has **19** answers

Since the line is perpendicular to another line with slope 13, its slope will be 13's opposite reciprocal, or $-\frac{1}{13}$. So the line we are trying to find has the equation $y=-\frac{1}{13}x+b$. Since it passes through (7,8), it holds that $8=-\frac{7}{13}+b\Rightarrow b=111$.

So the final equation is $y=-\frac{1}{13}x+111$

So the final equation is $y=-\frac{1}{13}x+111$

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Given a set of linear Diophantine Equations (LDE's), where each equation is one of the following form:

Let $C$ be a positive integer constant. Also, the number of variables in each equation is exactly $C$.

1. ${a}_{i}+{b}_{i}+{c}_{i}.....=C$ or

2. ${a}_{i}+{b}_{i}+{c}_{i}.....=(C+1)$

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2. $\ge 0$

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Let $C$ be a positive integer constant. Also, the number of variables in each equation is exactly $C$.

1. ${a}_{i}+{b}_{i}+{c}_{i}.....=C$ or

2. ${a}_{i}+{b}_{i}+{c}_{i}.....=(C+1)$

For every such set of LDE problem instance, the problem is solvable iff, at least one such solution exists, such that each variable's assigned value in that solution is:

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Can someone help with the proof of the above statement (or counterexamples with some small $C$)?

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