Question 1160199
The following are a set of points, where there is one unknown value. Use linear interpolation to determine the unknown value, y. Provide your answer to two decimal places. 

({{{x[0]}}},{{{y[0]}}})=({{{10}}},{{{80}}})
 ({{{x[1]}}},{{{y[1]}}})=({{{40}}},{{{5}}})
 ({{{x}}},{{{y}}})=({{{x}}},{{{43.85}}})

all points lie on same line

find equation of the line using two of the given points

The equation of a line is typically written as {{{y=mx+b}}}where {{{m}}} is the slope and {{{b}}} is the y-intercept.

first use points to find the slope {{{m}}} 

{{{m=(y[1]-y[0])/(x[1]-x[0])}}} 

{{{m=(5-80)/(40-10)}}} 

{{{m=-75/30}}} 

{{{m=-5/2}}} 

so far your equation is:

 {{{y=-(5/2)x+b}}}.........use one point to calculate {{{b}}}

 {{{5=-(5/2)40+b}}}

{{{5=-5*20+b}}}
{{{5=-100+b}}}
{{{b=5+100}}}

{{{b=105}}}


your equation is:

 {{{y=-(5/2)x+105}}}

now calculate missing coordinate  ({{{x}}},{{{43.85}}})

 {{{43.85=-(5/2)x+105}}}

{{{43.85-105=-(5/2)x}}}

{{{-61.15=-(5/2)x}}}

{{{x=-61.15/(-5/2)}}}

{{{x=24.46}}}


answer:

 ({{{24.46}}},{{{43.85}}})


{{{drawing ( 600, 600, -100, 100, -100, 100, 
circle(10,80,.7),locate(10,80,p(10,80)),
circle(40,5,.7),locate(40,5,p(40,5)),
circle(24.46,43.85,.7),locate(24.46,43.85,p(24.46,43.85)),
graph( 600, 600, -100, 100, -100, 100, -(5/2)x+105)) }}}