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