Question 217648

If you want to find the equation of line with a given a slope of {{{13/16}}} which goes through the point ({{{18}}},{{{13}}}), 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-13=(13/16)(x-18)}}} Plug in {{{m=13/16}}}, {{{x[1]=18}}}, and {{{y[1]=13}}} (these values are given)



{{{y-13=(13/16)x+(13/16)(-18)}}} Distribute {{{13/16}}}



{{{y-13=(13/16)x-117/8}}} Multiply {{{13/16}}} and {{{-18}}} to get {{{-117/8}}}



{{{y=(13/16)x-117/8+13}}} Add 13 to  both sides to isolate y



{{{y=(13/16)x-13/8}}} Combine like terms {{{-117/8}}} and {{{13}}} to get {{{-13/8}}} (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 with a slope of {{{13/16}}} which goes through the point ({{{18}}},{{{13}}}) is:



{{{y=(13/16)x-13/8}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=13/16}}} and the y-intercept is {{{b=-13/8}}}