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.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 left of the line is shaded.

Answer 1

She needs 6x + 8y ≥ 48. Solve for y: y ≥ 6 − (3/4)x, the line y = 6 − (3/4)x goes through (0,6) and (8,0), and the region satisfying ≥ is above (north of) that line. That corresponds to the graph with the line through (0,6) and (8,0) and everything to the left of the line shaded (the fourth option).