The table shows the amount maggie earns for various numbers of hours she babysits. graph the data. then find the slope of the line. explain what the slope represents. number of hours, 1, 2, 3, 4, and earnings $, 8, 16, 24, 32.

 The required slope of the line is 8 and it represents that the earning of Maggie per hour is $8.

Step-by-step explanation:  Given that the following table shows the amount Maggie earns for various numbers of hours she babysits :

Number of hours               1                 2                 3                   4

Earnings                            8                 16                24                32

We are to graph the data and to find the slope of the line.

From the table, we note that the points on the line representing the data are (1, 8), (2, 16), (3, 24) and (4, 32).

These points are plotted on the co-ordinate plane and its graph is shown on the attached figure below.

Now, the slope of a line passing through the points (a, b) and (c, d) is given by

So, the slope of the line representing the data is

Thus, the required slope of the line is 8 and it represents that the earning of Maggie per hour is $8.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is