Question

Taylor works at a garden shop that sells flower pots. One kind of flower pot has a rim height of 6 centimeters and a planting height of 22 centimeters. Taylor begins to stack the flower pots as shown.
The table shows the height of each stack for the given number of flower pots.

Number of Flower Pots, n 1 2 3 4 5
Height of Stack in cm 28 34 40 46 52
Write a simplified algebraic expression to represent the height of a stack of n flower pots.

Answer 1

Answer:

The simplified algebraic expression to represent the height, h, of a stack in cm of n flower pots is h = 6·n + 22

Step-by-step explanation:

The given information are;

The rim height of one kind of flower pot = 6 cm

The planting height of the flower pot = 22 cm

Therefore, the total height of the flower pot = 22 + 6 = 28 cm

Stacking the flower pots of a single kind will give a linear relationship of the form, y = m·x + c between the height of the stack and the number of flower pots in the stack

Where;

m = The slope or the rate of change of the height with the number of flower pots in a stack which can be found from two points in the given table of values

c = The y-intercept or height at the start of the first stack

From the table of  values, for the first and the last points, we have;

m = (52 - 28)/(5 - 1) = 24/4 = 6

Which gives;

h - 52 = 6×(n - 5)

h = 6·n - 30 + 52 = 6·n + 22

h = 6·n + 22

Where;

h = The height of stack in cm

n = The number of flower pots

Therefore, by comparing to the general form of the equation of a straight line, y = m·x + c, the y-intercept, c = 22

The simplified algebraic expression to represent the height of a stack of n flower pots is therefore given as h = 6·n + 22.