Question

Do the following scenarios model the equation y=2x+5 there are initially 5 chickens on the farm. Each month thereafter the number of chickens is 2 times the number in the month before

Answer 1

Answer: Yes, the given scenarios model the equation
`y=2x+5.`

Step-by-step explanation: The given linear equation is

`y=2x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

`m=(7-5)/(1-0)\\\\\Rightarrow m=2.`

Therefore, the equation of the line is

`y-5=m(x-0)\\\\\Rightarrow y-5=2x\\\\\Rightarrow y=2x+5.`

Since the above equation is same as equation (i), so the answer is YES.

The given scenario model the equation
`y=2x+5.`