Question

If $6\ge x\ge -2$ and $4\ge y\ge -4$, find the limits for $\frac{y}{x},$ where x and y are non-zero integers.

• A. $\frac{y}{x}\ge 2,\frac{y}{x}\le \frac{2}{3}$
• B. $\frac{y}{x}\ge \frac{-2}{3},\frac{y}{x}\le 2$
• C. $\frac{y}{x}\ge \frac{-2}{3},\frac{y}{x}\le \frac{1}{4}$
• D. $\frac{y}{x}\ge -4,\frac{y}{x}\le 4$

Answer 1

The correct option is D $\frac{y}{x}\ge -4,\frac{y}{x}\le 4$

y = 4 3 2 1 -1 -3 -4
x = 6 5 4 3 1 -1 -2
Hence, minimum value of $\frac{y}{x}=\frac{4}{-1}=-4$
And maximum value of $\frac{y}{x}=\frac{4}{1}=4$
$\therefore \frac{y}{x}\ge -4and\frac{y}{x}\le 4$.