Question 93248
First find the equation of the line passing through (-8,7) and (-2,0)



We can find the slope through the points ({{{-8}}},{{{7}}}) and ({{{-2}}},{{{0}}}) using this formula:


{{{m=(y[2]-y[1])/(x[2]-x[1])}}} 


{{{m=(0-7)/(-2--8)}}} Plug in {{{y[2]=0}}},{{{y[1]=7}}},{{{x[2]=-2}}},{{{x[1]=-8}}}  (these are the coordinates of given points)


{{{m= -7/6}}} Subtract the terms in the numerator {{{0-7}}} to get {{{-7}}}.  Subtract the terms in the denominator {{{-2--8}}} to get {{{6}}}

  

So the slope is

{{{m=-7/6}}}


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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
{{{y-y[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(\textrm{x_{1},y_{1}}\right)] is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


{{{y-7=(-7/6)(x--8)}}} Plug in {{{m=-7/6}}}, {{{x[1]=-8}}}, and {{{y[1]=7}}} (these values are given)



{{{y-7=(-7/6)(x+8)}}} Rewrite {{{x--8}}} as {{{x+8}}}



{{{y-7=(-7/6)x+(-7/6)(8)}}} Distribute {{{-7/6}}}


{{{y-7=(-7/6)x-28/3}}} Multiply {{{-7/6}}} and {{{8}}} to get {{{-56/6}}}. Now reduce {{{-56/6}}} to get {{{-28/3}}}


{{{y=(-7/6)x-28/3+7}}} Add {{{7}}} to  both sides to isolate y


{{{y=(-7/6)x-7/3}}} Combine like terms {{{-28/3}}} and {{{7}}} to get {{{-7/3}}} (note: if you need help with combining fractions, check out this <a href=http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver>solver</a>)



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Answer:



So the equation of the line which goes through the points ({{{-8}}},{{{7}}}) and ({{{-2}}},{{{0}}})  is:{{{y=(-7/6)x-7/3}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-7/6}}} and the y-intercept is {{{b=-7/3}}}


Notice if we graph the equation {{{y=(-7/6)x-7/3}}} and plot the points ({{{-8}}},{{{7}}}) and ({{{-2}}},{{{0}}}),  we get this: (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{drawing(500, 500, -14, 4, -5.5, 12.5,
graph(500, 500, -14, 4, -5.5, 12.5,(-7/6)x+-7/3),
circle(-8,7,0.12),
circle(-8,7,0.12+0.03),
circle(-2,0,0.12),
circle(-2,0,0.12+0.03)
) }}} Graph of {{{y=(-7/6)x-7/3}}} through the points ({{{-8}}},{{{7}}}) and ({{{-2}}},{{{0}}})



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Now lets find the equation of the perpendicular line through (5,8)



*[invoke equation_parallel_or_perpendicular "perpendicular", "-7/6", "-7/3", 5, 8]