Question 202961

First let's find the slope of the line through the points *[Tex \LARGE \left(-7,-5\right)] and *[Tex \LARGE \left(-3,-2\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-7,-5\right)]. So this means that {{{x[1]=-7}}} and {{{y[1]=-5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,-2\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=-2}}}.



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



{{{m=(-2--5)/(-3--7)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=-5}}}, {{{x[2]=-3}}}, and {{{x[1]=-7}}}



{{{m=(3)/(-3--7)}}} Subtract {{{-5}}} from {{{-2}}} to get {{{3}}}



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



So the slope of the line that goes through the points *[Tex \LARGE \left(-7,-5\right)] and *[Tex \LARGE \left(-3,-2\right)] is {{{m=3/4}}}



Now let's use the point slope formula:



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



{{{y--5=(3/4)(x--7)}}} Plug in {{{m=3/4}}}, {{{x[1]=-7}}}, and {{{y[1]=-5}}}



{{{y--5=(3/4)(x+7)}}} Rewrite {{{x--7}}} as {{{x+7}}}



{{{y+5=(3/4)(x+7)}}} Rewrite {{{y--5}}} as {{{y+5}}}



{{{y+5=(3/4)x+(3/4)(7)}}} Distribute



{{{y+5=(3/4)x+21/4}}} Multiply



{{{y=(3/4)x+21/4-5}}} Subtract 5 from both sides. 



{{{y=(3/4)x+1/4}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.




So the equation that goes through the points *[Tex \LARGE \left(-7,-5\right)] and *[Tex \LARGE \left(-3,-2\right)] is {{{y=(3/4)x+1/4}}}