Question 118003


If you want to find the equation of line with a given a slope of {{{3/7}}} which goes through the point ({{{-1}}},{{{-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=(3/7)(x--1)}}} Plug in {{{m=3/7}}}, {{{x[1]=-1}}}, and {{{y[1]=-2}}} (these values are given)



{{{y+2=(3/7)(x--1)}}} Rewrite {{{y--2}}} as {{{y+2}}}



{{{y+2=(3/7)(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y+2=(3/7)x+(3/7)(1)}}} Distribute {{{3/7}}}


{{{y+2=(3/7)x+3/7}}} Multiply {{{3/7}}} and {{{1}}} to get {{{3/7}}}


{{{y=(3/7)x+3/7-2}}} Subtract 2 from  both sides to isolate y


{{{y=(3/7)x-11/7}}} Combine like terms {{{3/7}}} and {{{-2}}} to get {{{-11/7}}} (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 {{{3/7}}} which goes through the point ({{{-1}}},{{{-2}}}) is:


{{{y=(3/7)x-11/7}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=3/7}}} and the y-intercept is {{{b=-11/7}}}


Notice if we graph the equation {{{y=(3/7)x-11/7}}} and plot the point ({{{-1}}},{{{-2}}}),  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, -10, 8, -11, 7,
graph(500, 500, -10, 8, -11, 7,(3/7)x+-11/7),
circle(-1,-2,0.12),
circle(-1,-2,0.12+0.03)
) }}} Graph of {{{y=(3/7)x-11/7}}} through the point ({{{-1}}},{{{-2}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{3/7}}} and goes through the point ({{{-1}}},{{{-2}}}), this verifies our answer.