Question

The blue line of best fit for boys intersects the vertical axis at 55 centimeters and the point (12.5, 70). Which equation best describes the boy's line of best fit?

Answer 1

Y = 1.2X + 55

Explanation:

As the blue line is a straight line, so that the equation describing it has the following form:

Y = a.X + b (1)

As the blue line intersects the vertical axis at 55 cm, so that it crosses point A with
`X_(A) = 0; Y_(A) = 55` . As point A is on the blue line, so that:

+)
`Y_(A) = a.X_(A) +b`

=> 55 = a.0 + b

=> 55 = b

As the blue line intersects the pink line at point B(12.5; 70) so that
`X_(B) = 12.5; Y_(B) = 70` . As point B is on the blue line, so we have:

+)
`Y_(B) = a.X_(B) +b`

=> 70 = a*12.5 + b

As b = 55

=> 70 = 12.5*a + 55

=> 12.5* a = 70 - 55 = 15

=> a = 15/12.5 = 1.2

Replace a = 1.2 and b = 55 into equation (1), we have:

Y = 1.2X + 55