Question

Ms. Perry bought a plant and is tracking the height of the plant each week. If y represents the height of the plant, in inches, x weeks after she bought the plant, which of the following situations is represented by the table below?

Time (weeks) 2 4 6 8
Height of Plant (inches) 10 15 20 25

Answer 1

The correct answer is, "When Ms. Perry bought the plant, its height was 5 inches. The plant grew at the rate of 2.5 inches per week. "

Answer 2

When Ms. Perry bought the plant, its height was 5 inches. The plant grew at the rate of 2.5 inches per week.

Explanation:

The rate of change, or slope, represents the rate at which the height of the plant increased per week.

Use the points (2 , 10) and (4 , 15) from the table to calculate the rate of change, also known as the slope.

y2 - y1 = 15 inches-10 inches

x2 - x1 4 weeks-2 weeks

2.5 inches/1 week or 2.5 inches per week

So, the rate of change is 2.5 inches per week.

Now, find the y-intercept, b, by using the equation y = mx + b, where m is the slope of the line represented by the given table of values and (x , y) is any point on the line.

Substitute m = 2.5 and (x , y) = (2 , 10) in the above equation to find out the initial height of the plant.

y=mx+b

10=2.5 (2) + b

5=b or b=5

So, the initial height of the plant was 5 inches.

Therefore, the situation represented by the table is when Ms. Perry bought the plant, its height was 5 inches. The plant grew at the rate of 2.5 inches per week.