Question

An economist is studying the linear relationship between the selling price p, of a

Answer 1

Answer:

The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60

Step-by-step explanation:

The given data are as follows

x,      p($)

10,    52.5

25,   41.25

40,   30

60,   15

We note that a plot of the given points give a straight line graph indicating a linear relationship

The rate of change of p($) with x is given by slope, m in the following relation;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Which gives;

$Slope, \, m =\dfrac{41.25-52.5}{25-10} = \dfrac{30-41.25}{40-25} = \dfrac{15-30}{40-60} =-0.75$

Therefore, to write the equation in slope and intercept form, we have;

From the first point with coordinates (52.5, 10), we have

y - 52.5 = -0.75×(x - 10)

y = -0.75·x + 7.5 + 52.5 = -0.75·x + 60

The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60.