Growth Rate of Plants

A Linear System

Situation Statement

The growth rate of Lily's store-bought plant and Lucy's home-grown plant.

Variables


  • h = height (cm)
  • t = time (days)

Table 1

Lily’s Store-Bought Plant
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Correct Equations

  • h = 3t + 15 → slope/y-intercept form (y = mx +b)
  • 3t - h + 15 = 0 → standard form (Ax + Bx + C = 0)

Table 2

Lucy’s Home-Grown Plant
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Correct Equations

  • h = 4t → slope/y-intercept form (y = mx +b)
  • 4t - h = 0 → standard form (Ax + Bx + C = 0)

Graphic Solution of Intersect

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Explanation

The solution of of this linear system has coordinates of (15, 60), as this is where the two lines intersect. This point of intersection represents the height of the plants when the time is the same and it shows when Lucy's home-grown plant will be the same height as Lily's store-bought plant. Also, from this point on the home-grown plant will be taller than the store-bought plant.

Summary Statement

Lilly’s and Lucy’s plants will both be at a height of 60 cm in 15 days.