Question 469294


First let's find the slope of the line through the points *[Tex \LARGE \left(2,40\right)] and *[Tex \LARGE \left(4,50\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,40\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=40}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,50\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=50}}}.



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



{{{m=(50-40)/(4-2)}}} Plug in {{{y[2]=50}}}, {{{y[1]=40}}}, {{{x[2]=4}}}, and {{{x[1]=2}}}



{{{m=(10)/(4-2)}}} Subtract {{{40}}} from {{{50}}} to get {{{10}}}



{{{m=(10)/(2)}}} Subtract {{{2}}} from {{{4}}} to get {{{2}}}



{{{m=5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,40\right)] and *[Tex \LARGE \left(4,50\right)] is {{{m=5}}}



Now let's use the point slope formula:



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



{{{y-40=5(x-2)}}} Plug in {{{m=5}}}, {{{x[1]=2}}}, and {{{y[1]=40}}}



{{{y-40=5x+5(-2)}}} Distribute



{{{y-40=5x-10}}} Multiply



{{{y=5x-10+40}}} Add 40 to both sides. 



{{{y=5x+30}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(2,40\right)] and *[Tex \LARGE \left(4,50\right)] is {{{y=5x+30}}}