Question 207229


If you want to find the equation of line with a given a slope of {{{1/2}}} which goes through the point (3,-8), you can simply use the point-slope formula to find the equation:




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



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



{{{y--8=(1/2)(x-3)}}} Plug in {{{m=1/2}}}, {{{x[1]=3}}}, and {{{y[1]=-8}}} (these values are given)



{{{y+8=(1/2)(x-3)}}} Rewrite {{{y--8}}} as {{{y+8}}}



{{{y+8=(1/2)x+(1/2)(-3)}}} Distribute {{{1/2}}}



{{{y+8=(1/2)x-3/2}}} Multiply {{{1/2}}} and {{{-3}}} to get {{{-3/2}}}



{{{y=(1/2)x-3/2-8}}} Subtract 8 from  both sides to isolate y



{{{y=(1/2)x-19/2}}} Combine like terms {{{-3/2}}} and {{{-8}}} to get {{{-19/2}}}



------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line with a slope of {{{1/2}}} which goes through the point (3,-8) is {{{y=(1/2)x-19/2}}}