David keeps records of his monthly earnings. Last month he worked 140 hours and earned $3700. This month he worked 120 hours and earned $3200.

Step-by-step explanation:

Part A:

Rate of pay for David =

                                            =

                                            = $25

Part B:

If he worked for number of hours = x

Then the function representing the earning will be,

f(x) = 25x + b

For an ordered pair (120, 3200),

3200 = 25(120) + b

b = 3200 - 3000

b = 200

Therefore, function will be,

f(x) = 25x + 200

Part C:

"Slope = 25" means the rate of change in earnings per hour is $25.

Similarly, y-intercept 'b = 200' will represent the fixed amount earned by David in addition to the per hour earnings.

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