Question 178994

First let's find the slope of the line through the points *[Tex \LARGE \left(-5,2\right)] and *[Tex \LARGE \left(-4,3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-5,2\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-4,3\right)].



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



{{{m=(3-2)/(-4--5)}}} Plug in {{{y[2]=3}}}, {{{y[1]=2}}}, {{{x[2]=-4}}}, and {{{x[1]=-5}}}



{{{m=(1)/(-4--5)}}} Subtract {{{2}}} from {{{3}}} to get {{{1}}}



{{{m=(1)/(1)}}} Subtract {{{-5}}} from {{{-4}}} to get {{{1}}}



{{{m=1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,2\right)] and *[Tex \LARGE \left(-4,3\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-2=1(x--5)}}} Plug in {{{m=1}}}, {{{x[1]=-5}}}, and {{{y[1]=2}}}



{{{y-2=1(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y-2=1x+1(5)}}} Distribute



{{{y-2=1x+5}}} Multiply



{{{y=1x+5+2}}} Add 2 to both sides. 



{{{y=1x+7}}} Combine like terms. 



{{{y=x+7}}} Simplify



So the equation in slope intercept form that goes through the points *[Tex \LARGE \left(-5,2\right)] and *[Tex \LARGE \left(-4,3\right)] is {{{y=x+7}}}



Now let's convert {{{y=x+7}}} to standard form:



{{{y=x+7}}} Start with the given equation.



{{{y-x=7}}} Subtract {{{x}}} from both sides.



{{{-x+y=7}}} Rearrange the terms.



{{{x-y=-7}}} Multiply EVERY term by -1 to make the x coefficient positive.



======================================================


Answer:


So the slope intercept equation is {{{y=x+7}}} and the standard equation is  {{{x-y=-7}}}