Question

juniper springs conservation area
the equation for the line of best fit is ( y = 2x + 7 ). according to the equation, which of these statements is true?
the tortoise population increases by about 2 tortoises every year.
the tortoise population increases by about 2 tortoises every 7 years.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y = 2x+7\), \(m = 2\) and \(b = 7\).

Step2: Interpret the slope in the context of the problem

The slope \(m=\frac{\Delta y}{\Delta x}\). In the context of the problem, \(y\) represents the number of tortoises and \(x\) represents time (in years). So, \(m = 2=\frac{\text{Change in number of tortoises}}{\text{Change in time}}\). This means that for every 1 - unit increase in \(x\) (i.e., every year), \(y\) (the number of tortoises) increases by 2.

Answer:

The tortoise population increases by about 2 tortoises every year.