Question 1126939
{{{x}}}|{{{y}}}
{{{1}}}	|{{{3}}}
{{{2}}}	|{{{9}}}
{{{3}}}|{{{17}}}
{{{4	}}}|{{{27}}}
{{{5	}}}|{{{39}}}
{{{6	}}}|{{{54}}}


first plot all points: 

{{{drawing( 600,600, -10, 60, -10, 60,
circle(1,3,.29),circle(2,9,.29),circle(3,17,.29),circle(4,27,.29),
circle(5,39,.29),circle(6,54,.29),

 graph( 600,600, -10, 60, -10, 60, 0)) }}}

as you can see, there is no line that passes through all these points, they are not on same line; so, we can only find a best-fit line for a set of data

all we can do to turn this into a linear function {{{y=mx+b}}},is to choose two given points which are somehow in the middle and find a slope {{{m}}}:

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}...use points ({{{2}}},{{{9}}}) and ({{{5}}},	{{{39}}})


{{{m=(39-9)/(5-2)}}}

{{{m=30/3}}}

{{{m=10}}}

so far, your equation is {{{y=10x+b}}}

you need y-intercept {{{b}}}, so use one point and plug {{{x}}} and {{{y}}} value in {{{y=6x+b}}}

I will go with this one:({{{2}}},{{{9}}})

{{{9=10*2+b}}}

{{{9=20+b}}}

{{{9-20=b}}}

{{{b=-11}}}

and you have:{{{y=10x-11}}}


graph it and check if that line is the best fit for given points:


{{{drawing( 600,600, -10, 60, -10, 60,
circle(1,3,.29),circle(2,9,.29),circle(3,17,.29),circle(4,27,.29),
circle(5,39,.29),circle(6,54,.29),

 graph( 600,600, -10, 60, -10, 60, 10x-11)) }}}


so, the line {{{y=10x-11}}} is a best-fit line for given set of points