Question 481683

First let's find the slope of the line through the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-7,0\right)]. So this means that {{{x[1]=-7}}} and {{{y[1]=0}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(0,5\right)].  So this means that {{{x[2]=0}}} and {{{y[2]=5}}}.



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



{{{m=(5-0)/(0--7)}}} Plug in {{{y[2]=5}}}, {{{y[1]=0}}}, {{{x[2]=0}}}, and {{{x[1]=-7}}}



{{{m=(5)/(0--7)}}} Subtract {{{0}}} from {{{5}}} to get {{{5}}}



{{{m=(5)/(7)}}} Subtract {{{-7}}} from {{{0}}} to get {{{7}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,5\right)] is {{{m=5/7}}}



Now let's use the point slope formula:



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



{{{y-0=(5/7)(x--7)}}} Plug in {{{m=5/7}}}, {{{x[1]=-7}}}, and {{{y[1]=0}}}



{{{y-0=(5/7)(x+7)}}} Rewrite {{{x--7}}} as {{{x+7}}}



{{{y-0=(5/7)x+(5/7)(7)}}} Distribute



{{{y-0=(5/7)x+5}}} Multiply



{{{y=(5/7)x+5}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,5\right)] is {{{y=(5/7)x+5}}}



 Notice how the graph of {{{y=(5/7)x+5}}} goes through the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,5\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(5/7)x+5),
 circle(-7,0,0.08),
 circle(-7,0,0.10),
 circle(-7,0,0.12),
 circle(0,5,0.08),
 circle(0,5,0.10),
 circle(0,5,0.12)
 )}}} Graph of {{{y=(5/7)x+5}}} through the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,5\right)]