Question

The graph shows the height, y, in centimeters, of a plant after a certain number of weeks, x. Shania drew the line of best fit on the graph.
A graph titled Plant Height shows Number of Weeks on x axis and Height of Plant in cm on y axis. The scales on both x and y axes are shown from 0 to 5 at increments of 5. The graph shows dots at the ordered pairs 0, 1 and 0.5, 1.2 and 1, 1.4 and 1.5, 2 and 2, 2.4 and 2.5, 2.7 and 3, 3 and 3.5, 3.3 and 4, 3.5 and 4.5, 3.8 and 5, 4. A straight line joins the ordered pairs 0, 1 and 5, 4

What would most likely be the approximate height of the plant after 7 weeks?

5.2 centimeters
7.6 centimeters
8.7 centimeters
12.7 centimeters

Answer 1

You are given a a graph titled Plant Height that shows Number of Weeks on x axis and Height of Plant in cm on y axis. Plotting this and you will get an equation of y = 1.2792x - 0.1665 (I used excel using the given points from the above problem).

y = 1.2792x - 0.1665
y = 1.2792 (7) - 0.1665
y = 8.78 centimeters.

The most likely approximate height of the plant after 7 weeks is 8.7 centimeters.

Answer 2

Answer:

5.2 cm.

Step-by-step explanation:

Given :

Number of Weeks(x)     Height of Plant (y)

 0                                          1

0.5                                       1.2

  1                                         1.4

 1.5                                       2

  2                                        2.4

 2.5                                      2.7

  3                                        3

 3.5                                      3.3

  4                                        3.5

 4.5                                      3.8

  5                                         4

We are given that A straight line joins the ordered pairs 0, 1 and 5, 4

So, we will find the equation of line using two point slope form:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$(x_1,y_1)=(0,1)$

$(x_2,y_2)=(5,4)$

Substitute the values in the formula

$y-1=\frac{4-1}{5-0}(x-0)$

$y-1=\frac{3}{5}(x)$ ---A

Now we are supposed to find e the approximate height of the plant after 7 weeks.

Substitute  x = 7 in A

$y-1=\frac{3}{5}(7)$

$y=\frac{3}{5}(7)+1$

$y=5.2$

Hence  the approximate height of the plant after 7 weeks is 5.2 cm.