The suppliers will supply 3,300 units if the price is $350.00 and 3,800 units if the price becomes $410.00. Then the linear supply equation is p = ? s + ? .
To find the linear supply equation, we need to determine the equation's slope (represented by the variable 's') and the y-intercept (represented by the variable 'p').
Given:
Price (p) = $350.00 when supply (s) = 3,300 units.
Price (p) = $410.00 when supply (s) = 3,800 units.
To find the slope:
Use the formula for slope: m = (y2 - y1) / (x2 - x1)
Let's assign p1 = 350, p2 = 410, s1 = 3300, and s2 = 3800.
m = (p2 - p1) / (s2 - s1)
= (410 - 350) / (3800 - 3300)
= 60 / 500
= 0.12
Therefore, the slope (s) is 0.12.
To find the y-intercept:
We can use the point-slope form of a linear equation: y - y1 = m (x - x1)
Let's select one of the given points, such as (s1, p1) = (3300, 350).
Using the point-slope form:
p - p1 = m (s - s1)
p - 350 = 0.12 (s - 3300)
Now, let's simplify the equation:
p - 350 = 0.12s - 396
p = 0.12s - 396 + 350
p = 0.12s - 46
Therefore, the linear supply equation can be written as p = 0.12s - 46, where 'p' represents the price and 's' represents the supply.