An economist believes there is a linear relationship between the market price of a particular commodity and the number of units suppliers of the commodity are willing to bring to the marketplace. Two sample observations indicate that when the price equals $15 per unit, the weekly supply equals 30,000 units; and when the price equals $20 per unit, the weekly supply equals 48,000 units.(i) If price per unit, p, is plotted on the horizontal axis and the quantity supplied q is plotted on the vertical axis, determine the slope-intercept form of the equation of the line which passes through these two points. (ii) Interpret the slope of the equation in this application. (iii) Predict the weekly supply if the market price equals $25 per unit.
Answers
Given : when the price is equal $15 per unit the weekly supply equal 30,000 units and when the price is equal $20 per unit the weekly supply equal 48000 units
To Find : determine the slope intercept from
Solution:
price per unit P is plotted on the horizontal axis and the quantity supplied Q is plotted on the vertical Axis
slope intercept from = y = mx + c
y represents Q
x represent P
( x , y) ⇔ (P , Q)
( 15 , 30000) , (20 , 48000)
Slope = ( 48000 - 30000)/ (20 - 15) = 3600
y - 48000 = 3600(x - 20)
=> y - 48000 = 3600x - 72000
=> y = 3600x - 24000
y = 3600x - 24000 is the slope intercept from
or Q = 3600P - 24000
weekly supply if the market price equal $25 per unit
=> P = 25
Q = 3600 * 25 - 24000
=> Q = 66000 units
weekly supply = 66000 units if the market price equal $25 per unit
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