Question 124403
If the x-intercept is -1 and y-intercept is 8, then we have the point (-1,0) for the x-intercept and the point (0,8) for the y-intercept



So let's find the equation of the line that goes through (-1,0) and (0,8)



First lets find the slope through the points ({{{-1}}},{{{0}}}) and ({{{0}}},{{{8}}})


{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula (note: *[Tex \Large \left(x_{1},y_{1}\right)] is the first point ({{{-1}}},{{{0}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{0}}},{{{8}}}))


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


{{{m= 8/1}}} Subtract the terms in the numerator {{{8-0}}} to get {{{8}}}.  Subtract the terms in the denominator {{{0--1}}} to get {{{1}}}

  


{{{m=8}}} Reduce

  

So the slope is

{{{m=8}}}


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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-0=(8)(x--1)}}} Plug in {{{m=8}}}, {{{x[1]=-1}}}, and {{{y[1]=0}}} (these values are given)



{{{y-0=(8)(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-0=8x+(8)(1)}}} Distribute {{{8}}}


{{{y-0=8x+8}}} Multiply {{{8}}} and {{{1}}} to get {{{8}}}


{{{y=8x+8+0}}} Add {{{0}}} to  both sides to isolate y


{{{y=8x+8}}} Combine like terms {{{8}}} and {{{0}}} to get {{{8}}} 


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Answer:



So the equation of the line which goes through the points ({{{-1}}},{{{0}}}) and ({{{0}}},{{{8}}})  is:{{{y=8x+8}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=8}}} and the y-intercept is {{{b=8}}}


Notice if we graph the equation {{{y=8x+8}}} and plot the points ({{{-1}}},{{{0}}}) and ({{{0}}},{{{8}}}),  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, -9.5, 8.5, -5, 13,
graph(500, 500, -9.5, 8.5, -5, 13,(8)x+8),
circle(-1,0,0.12),
circle(-1,0,0.12+0.03),
circle(0,8,0.12),
circle(0,8,0.12+0.03)
) }}} Graph of {{{y=8x+8}}} through the points ({{{-1}}},{{{0}}}) and ({{{0}}},{{{8}}})


Notice how the two points lie on the line. This graphically verifies our answer.