Question

GARDENING Simone planted a tomato plant and measured its height weekly. The total height at 2, 3, 4, and 5 weeks respectively were 13, 16, 19, and 22 inches tall. How tall was the tomato plant when Simone planted it? Assume the relationship is linear.

Answer 1

Since the relationship it is linear we can find the equation that represents the growing of the plant, and then calculate the initial value. The linear equation form is: y= m*x + b. We need to calculate the slope (m) first, with a pair of points, let's choose (2,13) and (4,19).

Using the formula for the slope we have:

`m=(y2-y1)/(x2-x1)=(19-13)/(4-2)=(6)/(2)=3`

With the slope, which is equal to 3 and any point, let's use (2,13) we can find the parameter b.

y= m*x + b

13= 3*(2) + b (Replacing the values)

13 = 6 + b (Multiplying)

13 -6 = b (Subtracting 6 on both sides of the equation)

7= b

Since b is the y-intercept then it is the initial value, it means that 7 was the height of the plant when it was planted.