Growth Rate of Plants
A Linear System
The growth rate of Lily's store-bought plant and Lucy's home-grown plant.
- h = height (cm)
- t = time (days)
Lily’s Store-Bought Plant
- h = 3t + 15 → slope/y-intercept form (y = mx +b)
- 3t - h + 15 = 0 → standard form (Ax + Bx + C = 0)
Lucy’s Home-Grown Plant
- h = 4t → slope/y-intercept form (y = mx +b)
- 4t - h = 0 → standard form (Ax + Bx + C = 0)
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.
Lilly’s and Lucy’s plants will both be at a height of 60 cm in 15 days.