economist believe there is a linear relationship between the market price of a particular community and the number of units supplies of the community are willing to bring to the market place to sample observation indicate when the price = $15 per unit the weekly supply = 30000 units and when the price = $20 per unit the weekly supply = 48000 units if the 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 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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