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Option B) h = 4.5t – 27 is the equation of the straight line that best models the height h, in centimeters, of the sunflower t days after it begins to grow.
From the above graph we can see that from day 14 to day 35 , it is a straight line.
And equation of a straight line is y = mx + c or y – y1 = m(x – x1)
Where, m =slope of the line
c = intercept
the equation can be rewritten as h – h1 = m(t – t1) (1)
So, to find the equation of line , first we will calculate the slope of the line.
To find the slope : m = (h2 – h1 ) / (t2 – t1) (2)
From the graph and the table given, the coordinates (t1 , h1 ) and ( t2 , h2 ) are (14 , 36.6) and (35, 131) respectively.
Putting these values in equation (2), we get
m = (131 – 36.6)/(35 – 14)
m = 94.4/21
m = 4.5
now to find the equation of line we put the values in equation (1), we get
h – 36.6 = 4.5(t – 14)
h – 36.6 = 4.5t – 63
h = 4.5t -63 + 36.6
h = 4.5t -27
Hence the equation of the line is , option B) h = 4.5t -27
Learn more about the straight line here : brainly.com/question/6977417
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