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

Let x = number of guests and y = pounds of meat. The caterer recommends y = (1/3)x − 2 and the customer wants at least that amount, so

y ≥ (1/3)x − 2.

The line y = (1/3)x − 2 goes through (0, −2) and (3, −1). Since the inequality is "≥", the region above the line is shaded. Therefore the correct graph is the fourth option: the dashed line through (0, −2) and (3, −1) with everything above (and to the left of, as described) the line shaded.