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?

Explanation:

Step1: Define the inequality

$6x + 8y \geq 48$

Step2: Simplify the inequality

Divide all terms by 2: $3x + 4y \geq 24$

Step3: Find intercepts (x=0)

$4y \geq 24 \implies y \geq 6$ (y-intercept at (0,6))

Step4: Find intercepts (y=0)

$3x \geq 24 \implies x \geq 8$ (x-intercept at (8,0))

Step5: Determine shaded region

Since we need values that are at least $48$, we shade the region above the line (all points that satisfy the inequality).

Answer:

The correct graph is the third one (top right): it has a line connecting (0,6) and (8,0), with the region above/including the line shaded.