The equation of the line of best fit is y=1.73x+0.0924. Based on the line of best fit, approximately how many pink flowers are predicted to bloom on a shrub with 40 red flow A. 23 B. 56 C. 69 D. 80 reserved.
The correct answer and explanation is:
Correct Answer: C. 69
To determine how many pink flowers are predicted to bloom on a shrub with 40 red flowers, substitute x = 40 into the line of best fit equation: y=1.73x+0.0924y = 1.73x + 0.0924 y=1.73(40)+0.0924y = 1.73(40) + 0.0924 y=69.2+0.0924=69.2924y = 69.2 + 0.0924 = 69.2924
Since the number of flowers must be a whole number and the value is approximately 69.29, it is reasonable to round this to 69.
Explanation:
A line of best fit is a linear equation that models the relationship between two variables. In this case, it is used to predict the number of pink flowers based on the number of red flowers on a shrub. The equation y = 1.73x + 0.0924 means that for every increase of 1 red flower, the number of pink flowers increases by approximately 1.73. The constant term 0.0924 is the y-intercept, representing the predicted number of pink flowers when there are zero red flowers, though this part of the model is more theoretical and often not meaningful in practical biological contexts.
To use this equation for a specific value, substitute the known x-value into the equation. Here, x is the number of red flowers, and it is given as 40. Multiplying 1.73 by 40 gives 69.2. Adding 0.0924 results in 69.2924. This value is very close to 69, and since you cannot have a fraction of a flower, it is rounded to the nearest whole number.
Therefore, the model predicts that approximately 69 pink flowers will bloom when a shrub has 40 red flowers, making the correct choice C.