First, we find the equation of the boundary line using the two intercepts.The slope is m = \(\frac{4 - 0}{0 - 5} = {4}{5}\) The y-intercept is 4 The slope-intercept form of the equation is therefore y = -\(\frac{4}{5} x + 4\) \(\implies y + \frac{4}{5} x = 4\) Multiply both sides by \(\frac{5}{4}\) \(\implies\frac{5}{4}(y +\frac{4}{5} x) = 4\times\frac{5}{4}\) \(\implies\frac{5}{4} y + x = 5\) Multiply both sides by 4 ⇒ \(5y + 4x = 20\) The inequality is therefore either \(5y + 4x \le 20\) or \(5y + 4x \ge 20.\) Using the test point (0, 0) -The origin ⇒ 5(0) + 4(0) \le 20 ⇒ 0 \le 20 (True) ∴ The inequality is \(5y + 4x \le 20\)