Answer:
Hence, the height of the plant after 7 weeks is:
5.2 centimeters.
Step-by-step explanation:
The graph shows the heights, y (in centimeters), of a plant after a certain number of weeks, x.
Shania drew the line of best fit on the graph.
We are asked to find what would be the approximate height of the plant after 7 weeks.
Clearly from the graph we could see that the line of best fit passes through the point:
(0,1) and (5,4)
we know that the equation of a line passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
(a,b)=(0,1) and (c,d)=(5,4)
Hence, the equation of line is:
[tex]y-1=\dfrac{4-1}{5-0}\times (x-0)\\\\y-1=\dfrac{3}{5}x\\\\y=\dfrac{3x}{5}+1[/tex]
Hence, the height of the plant after 7 weeks is evaluated by finding the value of y when x=7.
[tex]y=\dfrac{3}{5}\times 7+1\\\\y=\dfrac{3\times 7+1\times 5}{5}\\\\y=\dfrac{21+5}{5}\\\\y=\dfrac{26}{5}\\\\y=5.2 cm[/tex]
Hence, the height of the plant after 7 weeks is:
5.2 centimeters.
