$-6x < y + a$
In the $xy$ plane if the co-ordinates of the origin do not satisfy the above inequality, which one of the following would be true ?
- $a > 0$
- $a < 0$
- $a \leq 0$
- $a > 2$
- $a > 5$
How can I go about this without knowing the slope or the points or even the $y-\text{intercept}$ ?
Any pair of coordinates $(x,y)$ that does not satisfy the above inequality must satisfy the negation of the statement (opposite), i.e., $-6x\ge y+a$. Another way of writing this inequality is $y\le -6x-a$.
If you draw this inequality $y\le -6x-a$ for various values of $a$, you will see that the only possible values for $a$ that will include the origin are when $a\le 0$.