Question 189690

First let's find the slope of the line through the points *[Tex \LARGE \left(-9,0\right)] and *[Tex \LARGE \left(0,7\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-9,0\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(0,7\right)].



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



{{{m=(7-0)/(0--9)}}} Plug in {{{y[2]=7}}}, {{{y[1]=0}}}, {{{x[2]=0}}}, and {{{x[1]=-9}}}



{{{m=(7)/(0--9)}}} Subtract {{{0}}} from {{{7}}} to get {{{7}}}



{{{m=(7)/(9)}}} Subtract {{{-9}}} from {{{0}}} to get {{{9}}}



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



Now let's use the point slope formula:



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



{{{y-0=(7/9)(x--9)}}} Plug in {{{m=7/9}}}, {{{x[1]=-9}}}, and {{{y[1]=0}}}



{{{y=(7/9)(x--9)}}} Simplify



{{{y=(7/9)(x+9)}}} Rewrite {{{x--9}}} as {{{x+9}}}



{{{y=(7/9)x+(7/9)(9)}}} Distribute



{{{y=(7/9)x+7}}} Multiply



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



 Notice how the graph of {{{y=(7/9)x+7}}} goes through the points *[Tex \LARGE \left(-9,0\right)] and *[Tex \LARGE \left(0,7\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(7/9)x+7),
 circle(-9,0,0.08),
 circle(-9,0,0.10),
 circle(-9,0,0.12),
 circle(0,7,0.08),
 circle(0,7,0.10),
 circle(0,7,0.12)
 )}}} Graph of {{{y=(7/9)x+7}}} through the points *[Tex \LARGE \left(-9,0\right)] and *[Tex \LARGE \left(0,7\right)]