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

Answer:

Refer the figure.

Step-by-step 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,

$6(0)+8y=48$

$y=\frac{48}{8}$

$y=6$

y-intercept is at (0,6)

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

$6x+8(0)=48$

$x=\frac{48}{6}$

$y=8$

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.

Answer 2

To graph this we find the x- and y-intercepts. The x-intercept would be at 8 and the y-intercept would be at 6.

Explanation:
The equation is 6x+8y=48. An x-intercept is the point where the data crosses the x-axis. All points on this line will have a y-coordinate of 0, so we replace y with 0 and solve:
6x+8(0)=48
6x=48.

Divide both sides by 6:
6x/6=48/6
x=8.
We go to 8 on the x-axis and plot the point.

A y-intercept is the point where the data crosses the y-axis. All points on this line will have an x-coordinate of 9, so we replace x with 0 and solve: 6(0)+8y=48
0+8y=48
8y=48.

Divide both sides by 8:
8y/8 = 48/8
y=6.

We go up to 6 on the y-axis and plot the point. We then draw a line through these two points.