Question 788853
EDIT: See SECOND ATTEMPT... also, for more condensed, verified, and with Point-Slope form.


This can give points, (x, y), and may choose x for inches of lawn, y for blades of grass.


Using that format, you assign points, (1,55) and (4,230).  A linear equation for these two points can be modeled with y=mx+b, where m is slope and b is y-intercept.


{{{m=(230-55)/(4-1)=175/3}}}


Find b using y-mx=b or b=y-mx for which you pick either point.  Let me use (1,55).

{{{b=55-(175/3)*1}}}
{{{b=55*3/3-175/3}}}
{{{b=(55-175)/3}}}
{{{b=-3.33333}}}----( Now Corrected )
{{{b=-10/3}}}


The linear equation which models this blades of grass description is {{{highlight(y=(175/3)x-10/3)}}}.

Give careful attention to how the variables were assigned.  Your question was, how many blades of grass, y, are in 3 inches of lawn, x.  This means, what is y when x=3?


{{{highlight(y=(175/3)3-10/3)}}}
(Now Corrected)


______________________________________________________________

SECOND ATTEMPT TO BE SURE

Identifying (x,y) points as Inches of Lawn, Blades of Grass:
(1,55) and (4,230)


Slope {{{m=(230-55)/(4-1)=175/3}}}


Use Point-Slope form and use (1,55):
{{{highlight(y-55=(175/3)(x-1))}}}


Find y when x=3, meaning when Inches of Lawn is 3:
{{{y-55=(175/3)(3-1)}}}
{{{y=55+(175/3)(3-1)=55+(175/3)2}}}
{{{y=55+116&2/3}}}
{{{highlight(y=171&2/3)}}}
Either {{{y=171}}} OR {{{y=172}}} blades of grass