Nicole's cleaning company uses a linear model to determine the amount they charge their clients. they charged $144 for a cleaning job that took 4 hours. they charged $188 for a cleaning job that took 6 hours. which equation could be used to determine the amount charged, c, for a cleaning job that takes t hours? a. c = 10t + 104b. c = 36t c. c = 44t + 56d. c = 22t + 56

D

Step-by-step explanation:

Let the following point represent the first job:  (4, $144).  Let (6, $188) represent the second.  Then we find the equation of the line through these two points.  As we go from (4, $144) to (6, $188), x increases by 2 and y increases by $44.  Thus, the slope of this line is m = rise/run = $44/(2 hrs), or $22/hr.

Using the slope-intercept formula for a  straight line, y = mx + b, we find the equation of this line by finding the y-intercept, b:

Subbing the given info ($22/hr for m, 4 hr for x and $144 for y), we get:

$144 = ($22/hr)(4 hr) + b, or

$144 = $88 + b, which yields b = $56.

Thus, the desired equation is y = mx + b, or y = ($22/hr)x + $56.  This matches the last answer (D)

range is infinite on both x and y axis positive and negative

step-by-step explanation: