Question 117148


If you want to find the equation of line with a given a slope of {{{-5/8}}} which goes through the point ({{{2}}},{{{5}}}), 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-5=(-5/8)(x-2)}}} Plug in {{{m=-5/8}}}, {{{x[1]=2}}}, and {{{y[1]=5}}} (these values are given)



{{{y-5=(-5/8)x+(-5/8)(-2)}}} Distribute {{{-5/8}}}


{{{y-5=(-5/8)x+5/4}}} Multiply {{{-5/8}}} and {{{-2}}} to get {{{5/4}}}


{{{y=(-5/8)x+5/4+5}}} Add 5 to  both sides to isolate y


{{{y=(-5/8)x+25/4}}} Combine like terms {{{5/4}}} and {{{5}}} to get {{{25/4}}} (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 {{{-5/8}}} which goes through the point ({{{2}}},{{{5}}}) is:


{{{y=(-5/8)x+25/4}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=-5/8}}} and the y-intercept is {{{b=25/4}}}


Notice if we graph the equation {{{y=(-5/8)x+25/4}}} and plot the point ({{{2}}},{{{5}}}),  we get (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, -7, 11, -4, 14,
graph(500, 500, -7, 11, -4, 14,(-5/8)x+25/4),
circle(2,5,0.12),
circle(2,5,0.12+0.03)
) }}} Graph of {{{y=(-5/8)x+25/4}}} through the point ({{{2}}},{{{5}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{-5/8}}} and goes through the point ({{{2}}},{{{5}}}), this verifies our answer.