Question 202960


If you want to find the equation of line with a given a slope of {{{7/8}}} which goes through the point (5, -2), 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--2=(7/8)(x-5)}}} Plug in {{{m=7/8}}}, {{{x[1]=5}}}, and {{{y[1]=-2}}} (these values are given)



{{{y+2=(7/8)(x-5)}}} Rewrite {{{y--2}}} as {{{y+2}}}



{{{y+2=(7/8)x+(7/8)(-5)}}} Distribute {{{7/8}}}



{{{y+2=(7/8)x-35/8}}} Multiply {{{7/8}}} and {{{-5}}} to get {{{-35/8}}}



{{{y=(7/8)x-35/8-2}}} Subtract 2 from  both sides to isolate y



{{{y=(7/8)x-51/8}}} Combine like terms {{{-35/8}}} and {{{-2}}} to get {{{-51/8}}} (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 {{{7/8}}} which goes through the point (5, -2) is:


{{{y=(7/8)x-51/8}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=7/8}}} and the y-intercept is {{{b=-51/8}}}