Question

card 8
sol, axel, and troy have each planted a sunflower seed. the graph below shows the height of each person’s plant, in centimeters, over time. whose plant is growing the fastest? explain your thinking.
graph with height (cm) on y - axis (0 - 6) and time (days) on x - axis (0 - 6), with lines for sol, axel, troy starting at (0,0)

Explanation:

Step1: Understand growth rate

In a height - time graph (linear relationship here), the growth rate is represented by the slope of the line. The formula for the slope of a line between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a line passing through the origin \((0,0)\) and a point \((x,y)\), the slope \(m = \frac{y}{x}\), which is the rate of growth (height per day). A steeper line means a larger slope, hence a faster growth rate.

Step2: Compare slopes visually

Looking at the graph, the line representing Sol's plant is steeper than the lines representing Axel's and Troy's plants. This means that for the same change in time (x - value), the change in height (y - value) for Sol's plant is greater than that for Axel's and Troy's plants. So, Sol's plant has a larger slope (growth rate).

Answer:

Sol's plant is growing the fastest because the line representing the height of Sol's plant over time is the steepest among the three lines (Sol's, Axel's, and Troy's), indicating a greater rate of change of height with respect to time (a larger slope), which means it grows more centimeters per day.