Question

Emma earns $6 each time she mows the lawn and $8 per hour for babysitting. She is saving up to buy a new pair of jeans that cost $48. If she mows the lawn x times and babysits for y hours, which graph shows the amount of work she needs to complete to earn at least enough to purchase the new jeans?

A graph titled Emma apostrophe s Work shows Mowed lawns on the x-axis, from 0 to 10, and Hours of babysitting on the y-axis, from 0 to 50. A solid line has a negative slope and goes through (0, 48) and (8, 0). Everything to the right of the line is shaded.

A graph titled Emma apostrophe s Work shows Mowed lawns on the x-axis, from 0 to 10, and Hours of babysitting on the y-axis, from 0 to 50. A solid line has a negative slope and goes through (0, 48) and (8, 0). Everything to the left of the line is shaded.

A graph titled Emma apostrophe s Work shows Mowed lawns on the x-axis, from 0 to 10, and Hours of babysitting on the y-axis, from 0 to 10. A solid line has a negative slope and goes through (0, 6) and (8, 0). Everything to the right of the line is shaded.

Answer 1

6x + 8y ≥ 48 → y ≥ 6 − (3/4)x. The boundary line is y = 6 − (3/4)x, which goes through (0,6) and (8,0), and the region satisfying the inequality is the area at or above that line.

So the correct graph is the third one (the line through (0,6) and (8,0) with the region on/above the line shaded).