Question 179006


First let's find the slope of the line through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-4,0\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-4,0\right)].



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



{{{m=(0-7)/(-4-3)}}} Plug in {{{y[2]=0}}}, {{{y[1]=7}}}, {{{x[2]=-4}}}, and {{{x[1]=3}}}



{{{m=(-7)/(-4-3)}}} Subtract {{{7}}} from {{{0}}} to get {{{-7}}}



{{{m=(-7)/(-7)}}} Subtract {{{3}}} from {{{-4}}} to get {{{-7}}}



{{{m=1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-4,0\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-7=1(x-3)}}} Plug in {{{m=1}}}, {{{x[1]=3}}}, and {{{y[1]=7}}}



{{{y-7=1x+1(-3)}}} Distribute



{{{y-7=1x-3}}} Multiply



{{{y=1x-3+7}}} Add 7 to both sides. 



{{{y=1x+4}}} Combine like terms. 



{{{y=x+4}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-4,0\right)] is {{{y=x+4}}}



 Notice how the graph of {{{y=x+4}}} goes through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-4,0\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,x+4),
 circle(3,7,0.08),
 circle(3,7,0.10),
 circle(3,7,0.12),
 circle(-4,0,0.08),
 circle(-4,0,0.10),
 circle(-4,0,0.12)
 )}}} Graph of {{{y=x+4}}} through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-4,0\right)]