MATH SOLVE

10 months ago

Q:
# The two representative points for the first half of a data in a data set are (1,10) and (8,2). Create a data set with at least eight points that fits these representative points and find the line of best fit for the data.

Accepted Solution

A:

Answer:line : 8x+7y=78.points: (0 , 78/7) ,(78/8 , 0) , (2 , 62/7) ,etc.Step-by-step explanation:we have two points. so, we can find the equation of line passing through these 2 pointsthe equation of a line passing through the two points P(a,b) and Q(c,d)is : [tex]y-b=(\frac{d-b}{c-a} )*(x-a)\\[/tex]here, the equation of line passing through the given two points is [tex]y-10=(\frac{2-10}{8-1} )*(x-1)\\[tex]y-10=(\frac{-8}{7} )*(x-1)[/tex]multiplying both sides by 7,7y-70=-8x+8\\8x+7y=78[/tex]therefore, the line of best fit for the data is 8x+7y=78. now make 8 points which satisfy above line equation( for easier way fix some value for x and substitute it in the above line equation then find corresponding y value. these x & y values will make a point. for more points , keep changing the values of x and find corresponding y values)(0 , 78/7) ,(78/8 , 0) , (2 , 62/7) ,etc.