What is the rate of change of the amount earned with respect to hours worked for this function?
2 answers:
Question:
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
Answer: 13 dollars per hour
Step-by-step explanation:
The rate of change (ROC) for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x2, y2)
Point b = (2, 26) = (x1, y1)
Calculating the gradient or slope :
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
= 13 dollars per hour
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From the information obtained from the question, two equations can be created:
Let x and z be the two numbers (parts)
. . . . (1)
. . . . (2)
By transposing (2), make 'z' the subject of the equation
. . . . (3)
By substituting (3) into equation (1) to find a value for x
⇒
∴ either
OR 
Thus x = 5 or x = 10
By substituting the values of x into (2) to find z
z + (5) = 15 OR z + (10) = 15
⇒ z = 10 OR z = 5
So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.
Let x and z be the two numbers (parts)
By transposing (2), make 'z' the subject of the equation
By substituting (3) into equation (1) to find a value for x
⇒
∴ either
Thus x = 5 or x = 10
By substituting the values of x into (2) to find z
z + (5) = 15 OR z + (10) = 15
⇒ z = 10 OR z = 5
So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.