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 market place to sample observation indicate that when the price equals $15 per unit the weekly supply equals 30,000 and when the price equal $20 per unit the weekly supply equals 48000 units (a) 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 to points.
Answers
Given : 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 market place
sample observation indicate that when the price equals $15 per unit the weekly supply equals 30,000 and
when the price equal $20 per unit the weekly supply equals 48000 units (a) if price per unit, p, is plotted on the horizontal axis and the quantity supplied q is plotted on the vertical axis,
To Find : the slope-intercept form of the equation of the line which passes through these to points.
Solution:
Slope = dy/dx or Δy/Δx or (y₂ - y₁)/(x₂ - x₁)
where y is vertical axis and x is horizontal axis
price per unit, p, is plotted on the horizontal axis
the quantity supplied q is plotted on the vertical axis,
=> Slope = Δq/Δp
Δq = 48000 - 30000 = 18000
Δp = 20 - 15 = 5
Slope = 18000/5 = 3600
q - 48000 = 3600 ( p - 20)
=> q - 48000 = 3600p - 72000
=> q = 3600p - 24000
equation of the line which passes through these to points.
q = 3600p - 24000
q = mp + c is slope intercept form
m = 3600 , c = - 240000
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