Question 170856
You're on the right track. However, you have the coordinates of the points mixed up. Think of it like this: "t" is the independent and "y" is the dependent variable. Why is "t" the independent variable? Since the time can be any positive value (which is NOT affected by the number of nations), this means that "t" is independent. Since "y" changes as "t" changes, this means that "y" is dependent on "t"



Remember, any point on a coordinate system follows the form 


(independent variable, dependent variable)



So this means that every point is in the form (t,y)



This means that the two points are really (0,51) and (42, 159)




So let's find the equation of the line through the points (0,51) and (42, 159)



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First let's find the slope of the line through the points *[Tex \LARGE \left(0,51\right)] and *[Tex \LARGE \left(42,159\right)]



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(159-51)/(42-0)}}} Plug in {{{y[2]=159}}}, {{{y[1]=51}}}, {{{x[2]=42}}}, and {{{x[1]=0}}}



{{{m=(108)/(42-0)}}} Subtract {{{51}}} from {{{159}}} to get {{{108}}}



{{{m=(108)/(42)}}} Subtract {{{0}}} from {{{42}}} to get {{{42}}}



{{{m=18/7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,51\right)] and *[Tex \LARGE \left(42,159\right)] is {{{m=18/7}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y-51=(18/7)(x-0)}}} Plug in {{{m=18/7}}}, {{{x[1]=0}}}, and {{{y[1]=51}}}



{{{y-51=(18/7)x+(18/7)(-0)}}} Distribute



{{{y-51=(18/7)x+0}}} Multiply



{{{y=(18/7)x+0+51}}} Add 51 to both sides. 



{{{y=(18/7)x+51}}} Combine like terms. 



{{{y=(18/7)x+51}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(0,51\right)] and *[Tex \LARGE \left(42,159\right)] is {{{y=(18/7)x+51}}}