Question

When planning for a party, one caterer recommends the amount of meat be 2 pounds fewer than One-third the total number of guests. The customer decides they want at least that amount of meat. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything below and to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything above and to the left of the line is shaded.

Answer 1

Answer: Let's break down the information given in the scenario to form the equation:

The amount of meat recommended by the caterer is 2 pounds fewer than one-third the total number of guests.

The customer wants at least that amount of meat.

Let's assume:

x represents the total number of guests (independent variable).

y represents the amount of meat (dependent variable).

From point 1, the equation for the recommended amount of meat can be written as:

y = (1/3)x - 2

Now, from point 2, the customer wants at least that amount of meat, which means the amount of meat should be greater than or equal to the recommended amount. So the equation representing the customer's demand is:

y >= (1/3)x - 2

Now, let's look at the given graphs:

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.

This line represents the equation y = x - 2, which is not the correct equation from our scenario. It has a different slope and intercept.

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the left of the line is shaded.

This line represents the equation y = -x - 2, which is also not the correct equation from our scenario. It has the wrong slope and intercept.

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything below and to the right of the line is shaded.

This line represents the equation y = x - 2, which is once again not the correct equation from our scenario. It has the correct intercept but a different slope.

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything above and to the left of the line is shaded.

This line represents the equation y = (1/3)x - 2, which is the correct equation from our scenario. The slope is 1/3 (positive slope) and the intercept is -2 (going through the point (0, -2)).

Therefore, the correct graph representing the overall equation represented by this scenario is: On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything above and to the left of the line is shaded.