Respuesta :
Answer: Yes, the given scenarios model the equation [tex]y=2x+5.[/tex]
Step-by-step explanation: The given linear equation is
[tex]y=2x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let x represents the number of months and y represents the corresponding number of chickens after x months on the firm.
Given that there are initially 5 chickens on the firm, so we have
when x = 0, then y = 5.
Also, since each month thereafter the number of chickens is 2 times the number in the month before, so
when x = 1, y = 5 + 2 = 7,
when x = 2, y = 7 + 2 = 9,
when x = 3, y = 9 + 2 = 11, etc.
So, (x, y) = (0, 5), (1, 7), (2, 9), (3, 11), etc. are points lying on the linear function described by x and y.
The slope of the line passing through the points (0, 5) and (1, 7) will be given by
[tex]m=\dfrac{7-5}{1-0}\\\\\Rightarrow m=2.[/tex]
Therefore, the equation of the line is
[tex]y-5=m(x-0)\\\\\Rightarrow y-5=2x\\\\\Rightarrow y=2x+5.[/tex]
Since the above equation is same as equation (i), so the answer is YES.
The given scenario model the equation [tex]y=2x+5.[/tex]
