Part iii: bailey works part-time at a movie theater. the theater pays employees an hourly wage based on their length of employment. write an algebraic expression that describes how much bailey’s employer pays part-time workers. length of employment (months) hourly wage (dollars/hour) 6 months                                           7.55 12 months                                         7.85 18 months                                         8.15 24 months                                         8.45

From the given table, the points can be written as : (6,7.55) , (12,7.85), (18, 8.15) and (24, 8.45)

Slope

m =

m = 0.05

slope intercept form of line =

We plug m = 0.05, x = 6 and y = 7.55 and find c.

c= 7.25

Required equation: ... Answer

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is