Question

Mark and Jessica are each making a linear model to predict the population of squirrels in the town park. The are both using the same data points to find an equation of the line of best fit: the squirrel population, p, in 2002 and the squirrel population, q, in 2011. Mark is using the year as the x-value, and he represents his data as (2002, p) and (2011, q). Jessica is using the years since 2000 as her x-value, and she represents her data as (2, p) and (11, q).
Which statement best describes how their prediction equations compare?

A. Their equations have the same x-coefficients and y-intercepts.
B. Their equations have different x-coefficients and y-intercepts.
C. Their equations have different y-intercepts but the same x-coefficients.
D. Their equations have the same y-intercepts but different x-coefficients.

Answer 1

A........3x + 2y = 24

Answer 2

Answer:  The answer is (C) Their equations have different y-intercepts but the same x-coefficients.

Step-by-step explanation:  Given that Mark and Jessica are each making a linear model to predict the population of squirrels in the town park.

Since (2002, p) and (2011, q) are two points on Mark's data, so the linear equation representing the population of squirrels is given by

$y-p=\dfrac{q-p}{2011-2002}(x-2002)\\\\\\\Rightarrow y-p=\dfrac{q-p}{9}(x-2002)\\\\\\\Rightarrow y-p=x\left(\dfrac{q-p}{9}\right)-\dfrac{2002(q-p)}{9}\\\\\\\Rightarrow y=x\left(\dfrac{q-p}{9}\right)-\dfrac{2002(q-p)}{9}+p~~~~~~~~~~(i)$

Also, (2, p) and (11, q) are two points on Jessica's data, so the linear equation will be

$y-p=\dfrac{q-p}{11-2}(x-2)\\\\\\\Rightarrow y-p=\dfrac{q-p}{9}(x-2)\\\\\\\Rightarrow y-p=x\left(\dfrac{q-p}{9}\right)-\dfrac{2(q-p)}{9}\\\\\\\Rightarrow y=x\left(\dfrac{q-p}{9}\right)-\dfrac{2(q-p)}{9}+p~~~~~~~~~~(ii)$

Comparing equations (i) and (ii), we can say that Mark and Jessica's linear equations have different y-intercepts but same x-coefficients.

Thus, (C) is the correct option.