Question 150342

First let's find the slope of the line through the points *[Tex \LARGE \left(42,20\right)] and *[Tex \LARGE \left(52,10\right)]



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



{{{m=(10-20)/(52-42)}}} Plug in {{{y[2]=10}}}, {{{y[1]=20}}}, {{{x[2]=52}}}, {{{x[1]=42}}}, , 



{{{m=(-10)/(52-42)}}} Subtract {{{20}}} from {{{10}}} to get {{{-10}}}



{{{m=(-10)/(10)}}} Subtract {{{42}}} from {{{52}}} to get {{{10}}}



{{{m=-1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(42,20\right)] and *[Tex \LARGE \left(52,10\right)] is {{{m=-1}}}



Now let's use the point slope formula:



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



{{{y-20=-1(x-42)}}} Plug in {{{m=-1}}}, {{{x[1]=42}}}, and {{{y[1]=20}}}



{{{y-20=-1x+-1(-42)}}} Distribute



{{{y-20=-1x+42}}} Multiply



{{{y=-1x+42+20}}} Add 20 to both sides. 



{{{y=-1x+62}}} Combine like terms. 



{{{y=-x+62}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(42,20\right)] and *[Tex \LARGE \left(52,10\right)] is {{{y=-x+62}}}