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?

Answer 1

Refer the figure.

Explanation:

Let x be the number of times Emma mows the lawn

and y be the number of hours Emma babysits

Emma earns $6 each time she mows the lawn and $8 per hour for babysitting i.e.
`6x+8y`

She is saving up to buy a new pair of jeans that cost $48.

i.e.
`6x+8y\geq 48`

The y-intercept of the line is the point when x=0,

`6(0)+8y=48`

`y=(48)/(8)`

`y=6`

y-intercept is at (0,6)

The x-intercept of the line is the point when y=0,

`6x+8(0)=48`

`x=(48)/(6)`

`y=8`

x-intercept is at (8,0).

The shaded area is determined by putting x and y zero.

`6(0)+8(0)\geq 48`

`0\geq 48`

False so the region is away from origin.

The solution is the shade area above the solid line.

Refer the attached figure.