Question

The price of a share of stock in XYZ Corporation was $74 two weeks ago. Seven weeks ago, the price

Answer 1

a) The linear equation to find the price p of a share of XYZ Corporation stock w weeks from now is p = 3w + b

b) Price of a share of stock five weeks ago is $ 65

Solution:

The equation of line (in slope intercept form) is given as:

y = mx + b

Where "m" is the slope and "b" is the y - intercept

The equation of a line for price p of a share of XYZ Corporation stock w weeks from now is:

p = mw + b

where y = the price of the stock, w = weeks, m is the slope and b is the y-intercept and "p" is the price of share

Given that  price of a share of stock in XYZ Corporation was $74 two weeks ago. Seven weeks ago, the price  was $59 a share

So we have two points (-2, 74) and (-7, 59)

The slope "m" can be found as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text{ here } x_1 = -2 ; y_1 = 74 ; x_2 = -7 ; y_2 = 59$

$\begin{aligned}m &=\frac{59-74}{-7-(-2)} \\\\m &=\frac{-15}{-5}=3\end{aligned}$

Thus the equation becomes:

p = 3w + b

To find b, plug in either known point:

Substitute (w, p) = (-2, 74)

74 = 3(-2) + b

74 = -6 + b

b = 80

Thus equation becomes:

p = 3w + 80

b. Estimate the price of a share of stock five weeks ago

Here w = -5

p = 3(-5) + 80

p = -15 + 80

p = 65

Thus price of a share of stock five weeks ago is $ 65