Here’s the step-by-step breakdown of solving the given task:

Problem Recap:

• Total income needed: $1,475 per month
• Work-hour constraints: A maximum of 172 hours per month
• Two jobs:
  • Job 1 pays $8.25/hour → work $x$ hours.
  • Job 2 pays $9.00/hour → work $y$ hours.

Step 1: Write the inequalities

1. Total hours worked constraint: $x + y \leq 172$ (You cannot work more than 172 hours in a month.)

2. Income constraint: $8.25x + 9.00y \geq 1475$ (You must earn at least $1,475.)

Step 2: Graph the inequalities

Coordinate system:

• $x$: hours worked at $8.25/hour.
• $y$: hours worked at $9.00/hour.

Steps to graph:

1. Plot the boundary line for $x + y = 172$:

   • When $x = 0$, $y = 172$ (point: $(0, 172)$).
   • When $y = 0$, $x = 172$ (point: $(172, 0)$).

2. Plot the boundary line for $8.25x + 9y = 1475$:

   • When $x = 0$, $y = \frac{1475}{9} \approx 163.89$ (point: $(0, 163.89)$).
   • When $y = 0$, $x = \frac{1475}{8.25} \approx 178.79$ (point: $(178.79, 0)$).

3. Shade:

   • For $x + y \leq 172$, shade below the line $x + y = 172$.
   • For $8.25x + 9y \geq 1475$, shade above the line $8.25x + 9y = 1475$.

4. Identify the feasible region: It is the overlapping shaded area satisfying both constraints.

Would you like me to create the graph for you? Let me know! 😊