Chapter 11.7, Problem 53AYU

In problems 53-56, write a system of linear inequalities for the given graph.

To determine

To write: A system of linear inequalities for the given graph.

Answer to Problem 53AYU

Solution:

$x \ge 0, y \ge 0, x \le 4, x + y \le 6$

Explanation of Solution

Formula Used:

Equation of a line is $y = mx + b$

Where $m = slope = \frac{y_2 - y_1}{x_2 - x_1}$ (if two points $\left(x_1, y_1\right), \left(x_2, y_2\right)$ are given)

$b = y - intercept$.

Given:

Graph with feasible points.

Calculation:

From the graph, it can be see that

$x \ge 0$

$y \ge 0$

$x \le 4$

To find equation of a line passes through $\left(4, 2\right), \left(0, 6\right)$.

From formula used $m = - 4/4 = - 1$

$b = 6$

$y = - x + 6$

Therefore, $x + y \le 6$ (from the graph).