Question 146134


First let's find the slope through the points *[Tex \LARGE \left(30,136\right)] and *[Tex \LARGE \left(70,104\right)]



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



{{{m=(104-136)/(70-30)}}} Plug in {{{y[2]=104}}}, {{{y[1]=136}}}, {{{x[2]=70}}}, {{{x[1]=30}}}, , 



{{{m=(-32)/(70-30)}}} Subtract {{{136}}} from {{{104}}} to get {{{-32}}}



{{{m=(-32)/(40)}}} Subtract {{{30}}} from {{{70}}} to get {{{40}}}



{{{m=-4/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(30,136\right)] and *[Tex \LARGE \left(70,104\right)] is {{{m=-4/5}}}



This means that the rate of change is {{{m=-4/5}}}



Now let's use the point slope formula to find the equation of the line:



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



{{{y-136=(-4/5)(x-30)}}} Plug in {{{m=-4/5}}}, {{{x[1]=30}}}, and {{{y[1]=136}}}



{{{y-136=(-4/5)x+(-4/5)(-30)}}} Distribute



{{{y-136=(-4/5)x+24}}} Multiply



{{{y=(-4/5)x+24+136}}} Add 136 to both sides. 



{{{y=(-4/5)x+160}}} Combine like terms. 



{{{y=(-4/5)x+160}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(30,136\right)] and *[Tex \LARGE \left(70,104\right)] is {{{y=(-4/5)x+160}}}