you are orderning shirts for the math club at your school. Short-sleeved Shirts cost $\$ 8$ each. Long sleeved Shirts cost $\$ 20$ each. You have a budget of $\$ 200$ for the shirts. The equation $8 x+20 y=200$ models the total cost, where $x$ is the number of Short-sleeved Shirts and $y$ is the number of $10 \mathrm{ng}-$ steeved shirts. Graph the equation. Interphet the intercepts.

Step 1 ：First, we need to understand the given equation \(8x + 20y = 200\), where \(x\) is the number of short-sleeved shirts and \(y\) is the number of long-sleeved shirts.

Step 2 ：To graph the equation, we first need to find the intercepts.

Step 3 ：The x-intercept is found by setting \(y = 0\) and solving for \(x\). So, \(8x + 20(0) = 200\) simplifies to \(8x = 200\). Dividing both sides by 8 gives \(x = 25\). So, the x-intercept is (25, 0).

Step 4 ：The y-intercept is found by setting \(x = 0\) and solving for \(y\). So, \(8(0) + 20y = 200\) simplifies to \(20y = 200\). Dividing both sides by 20 gives \(y = 10\). So, the y-intercept is (0, 10).

Step 5 ：Now, we can plot these two points on a graph and draw a line through them to represent the equation.

Step 6 ：The x-intercept (25, 0) means that if all the shirts purchased are short-sleeved, then 25 shirts can be bought with the $200 budget.

Step 7 ：The y-intercept (0, 10) means that if all the shirts purchased are long-sleeved, then 10 shirts can be bought with the $200 budget.

Step 8 ：So, the intercepts represent the maximum number of each type of shirt that can be bought if all the money is spent on that type of shirt.