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

5.2 cm.

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=(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=(4-1)/(5-0)(x-0)`

`y-1=(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=(3)/(5)(7)`

`y=(3)/(5)(7)+1`

`y=5.2`

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

Answer 2

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.