Question

Which of the following ordered pairs is represented by the line $7x-5y-5=0$.

• A. $(6,7)$
• B. $(7,7)$
• C. $(5,6)$
• D. $(8,7)$

Answer 1

The correct option is C $(5,6)$

$7x-5y-5=0$ can be re-written as $\frac{7x-5}{5}=y$ or $\frac{7x}{5}-1=y$

Hence for integral values of both $x$ and $y{,}^{\prime }{x}^{\prime }$ has to be a multiple of $5$.

The smallest non-zero multiple of $5$ is $5$ itself.

For $x=5$, we get $y=7-1=6$.

Hence, $(5,6)$ satisfies the above equation.