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The graph shows the linear relationship between the height of a plant (in centimeters) and the time (in weeks) that the plant has been growing. Which statements are correct? Check all that apply. The rate of change is 4. The rate of change is 1. The rate of change is . The plant grows 4 cm in 1 week. The plant grows 1 cm in 4 weeks

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meerkat18
I found a graph with the same problem, so I guess this is the graph to be based on. To find the rate, just determine the slope between any two points along the line. Suppose these points are: (30,10) and (50,20).

Slope = (20 - 10)/(50 - 30) = 1/2

The correct answer should be: the rate of change is 1 cm per 2 weeks, or 1/2.
Ver imagen meerkat18

The rate of change will be 0.5 and the growth of the plant in 4 weeks will be 9cm and this can be determine by using the slope formula and point slope equation of the line.

Given :

  • Graph between Height (cm) and Time (days).
  • Points - (30,10) and (50,20)

The rate of change is given by the formula:

[tex]\dfrac{dh}{dt} = \dfrac{y_2-y_1}{x_2-x_1}[/tex]    ---- (1)

where, h is the height in cm, t is the time in days, and [tex](x_1,y_1)\;and \;(x_2,y_2)[/tex] are the points on the line.

Now, put the value of  [tex](x_1,y_1)\;and \;(x_2,y_2)[/tex] in equation (1).

[tex]\dfrac{dh}{dt} = \dfrac{20-10}{50-30}[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{10}{20}=\dfrac{1}{2}[/tex]

Therefore, the rate of change will be 0.5.

Now, the linear equation is given by:

[tex]\dfrac{y-y_1}{x-x_1} = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\dfrac{y-10}{x-30} = \dfrac{20-10}{50-30}[/tex]

[tex]y-10 = \dfrac{1}{2}(x-30)[/tex]

[tex]2y-20 = x-30[/tex]

2y = x - 10

The growth of the plant in 4 weeks will be:

2y = 28 - 10

2y = 18

y = 9cm

For more information, refer the link given below:

https://brainly.com/question/22122594

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