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Question

Function I is defined by the graph, function II is defined by the table, and function III is defined by the equation y=4.5x+9.


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The given options represent the functions in decreasing order based on their slopes. Choose the option correctly representing the order.

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Solution

Detailed step-by-step solution:
Finding the slope of function I:
Consider two points (1,1) and (0,3) on the graph.
SlopeI=RiseRun
=Change in yChange in y
=3(1)0(1)
=3+11
=4
Finding the slope of function II:
Consider two ordered pairs (1,14) and (2,19) from the table.
SlopeII=RiseRun
=Change in yChange in y
=191421
=51
=5
Finding the slope of function III: y=4.5x+9
For the equation y=mx+b
m= slope
Comparing y=4.5x+9 with y=mx+b, we get:
SlopeIII=m=4.5
5>4.5>4
SlopeII>SlopeIII>SlopeI
Decreasing order of the functions based on their slopes will be:
Function II > Function III > Function I
Option A is correct.

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