Question

two types of ornamental grass are being grown at a research center. the data showing the relationship between the height of the grass and the number of weeks of growth are represented for variety i and variety ii. variety i variety ii what is the unit rate, in centimeters per week, of the growth of the grass variety that grows faster?

Explanation:

Step1: Find the unit rate for Variety I

The unit rate (slope) for a linear relationship \(y = mx + b\) (where \(b = 0\) since at \(x = 0\), \(y=0\)) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Variety I, using the points \((x_1 = 0,y_1 = 0)\) and \((x_2=1,y_2 = 2)\), the slope \(m_1=\frac{2 - 0}{1 - 0}=2\) centimeters per week.

Step2: Find the unit rate for Variety II

Using two points from the graph of Variety II, say \((x_1 = 1,y_1 = 2)\) and \((x_2 = 2,y_2 = 5)\). The slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), so \(m_2=\frac{5 - 2}{2 - 1}=3\) centimeters per week.

Answer:

\(3\)