A scatter plot that represents the amount of miles that runners in a running club ran last week as well as their best mile time is shown below Graphed points: (19,7.4),(34,6.8),(38,6.2),(50,5.2) ,(56,5.7),(70,5.9),(78,4.4)

Malik wants to use the equation y=ax+b to represent a line of best fit for the data where x represents the amount of miles ran last week and y represents the best mile pace (in minutes). He wants to determine a line of best fit in order to estimate best mile paces for other runners.

Complete the table to determine which values should be used for a and b

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation:

i hope this is what you were looking for.

see attached graph