A study was conducted on the year and the number of honeybees in a beekeeper’s hive. After using the averaging method for the line of best fit, the two representative points found were (10, 250) and (20, 500). What is true about the line of best fit for this data? Select all that apply.

-The estimated slope is 25.
-The y-intercept is 0.
-The equation for the line of best fit of this data is y = 25x.
-The equation for the line of best fit of this data is y = -25x.
-The line passes through the two representative data points but may or may not pass through any of the data points.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that:-

A study was conducted on the year and the number of honeybees in a beekeeper’s hive. After using the averaging method for the line of best fit, the two representative points found were (10, 250) and (20, 500).

The equation of the line will be calculated as:-

The intercept of the line will be;-

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-250}{20-10}=25[/tex]

The equation of the line is given as:-

y - y₁ = m( x - x₁ )

Putting the coordinates:-

y - 250 = 25 ( x - 10 )

y - 250 = 25x - 250

y = 25x

Therefore the correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.

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