Question 111292


If you want to find the equation of line with a given a slope of {{{2}}} which goes through the point ({{{0}}},{{{-4}}}), 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--4=(2)(x-0)}}} Plug in {{{m=2}}}, {{{x[1]=0}}}, and {{{y[1]=-4}}} (these values are given)



{{{y+4=(2)(x-0)}}} Rewrite {{{y--4}}} as {{{y+4}}}



{{{y+4=2x+(2)(-0)}}} Distribute {{{2}}}


{{{y+4=2x+0}}} Multiply {{{2}}} and {{{-0}}} to get {{{0}}}


{{{y=2x+0-4}}} Subtract 4 from  both sides to isolate y


{{{y=2x-4}}} Combine like terms {{{0}}} and {{{-4}}} to get {{{-4}}} 

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Answer:



So the equation of the line with a slope of {{{2}}} which goes through the point ({{{0}}},{{{-4}}}) is:


{{{y=2x-4}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=2}}} and the y-intercept is {{{b=-4}}}


Notice if we graph the equation {{{y=2x-4}}} and plot the point ({{{0}}},{{{-4}}}),  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, -9, 9, -13, 5,
graph(500, 500, -9, 9, -13, 5,(2)x+-4),
circle(0,-4,0.12),
circle(0,-4,0.12+0.03)
) }}} Graph of {{{y=2x-4}}} through the point ({{{0}}},{{{-4}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{2}}} and goes through the point ({{{0}}},{{{-4}}}), this verifies our answer.