Question 172824

First let's find the slope of the line through the points *[Tex \LARGE \left(-2,0\right)] and *[Tex \LARGE \left(7,4\right)]



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



{{{m=(4-0)/(7--2)}}} Plug in {{{y[2]=4}}}, {{{y[1]=0}}}, {{{x[2]=7}}}, and {{{x[1]=-2}}}



{{{m=(4)/(7--2)}}} Subtract {{{0}}} from {{{4}}} to get {{{4}}}



{{{m=(4)/(9)}}} Subtract {{{-2}}} from {{{7}}} to get {{{9}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-2,0\right)] and *[Tex \LARGE \left(7,4\right)] is {{{m=4/9}}}



Now let's use the point slope formula:



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



{{{y-0=(4/9)(x--2)}}} Plug in {{{m=4/9}}}, {{{x[1]=-2}}}, and {{{y[1]=0}}}



{{{y=(4/9)(x--2)}}} Simplify



{{{y=(4/9)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y=(4/9)x+(4/9)(2)}}} Distribute



{{{y=(4/9)x+8/9}}} Multiply




So the equation that goes through the points *[Tex \LARGE \left(-2,0\right)] and *[Tex \LARGE \left(7,4\right)] is {{{y=(4/9)x+8/9}}}