Question 102658
"1) Write the equation y=1/3x - 2 in standard form using only integers and a positive coefficient for x.
a) x+3y=6 b) x-3y=2 c)-x+3y=-6 d)x-3y=6 "


*[invoke converting_linear_equations "slope-intercept_to_standard", 1, 2, 3, "1/3", -2]


Now if you want A to be positive, multiply both sides by -1



{{{-1(-x+3y)=-1(-6)}}}



{{{x-3y=6}}} Distribute and multiply



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"

20 Which of the following equations represents a line l that goes through (-1,-3) and has a slope of 4?

a)y=4x-3    b)y=4x+1     c)y=4x-1       d)y=4x+3"





If you want to find the equation of line with a given a slope of {{{4}}} which goes through the point ({{{-1}}},{{{-3}}}), 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--3=(4)(x--1)}}} Plug in {{{m=4}}}, {{{x[1]=-1}}}, and {{{y[1]=-3}}} (these values are given)



{{{y+3=(4)(x--1)}}} Rewrite {{{y--3}}} as {{{y+3}}}



{{{y+3=(4)(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y+3=4x+(4)(1)}}} Distribute {{{4}}}


{{{y+3=4x+4}}} Multiply {{{4}}} and {{{1}}} to get {{{4}}}


{{{y=4x+4-3}}} Subtract 3 from  both sides to isolate y


{{{y=4x+1}}} Combine like terms {{{4}}} and {{{-3}}} to get {{{1}}} 

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Answer:



So the equation of the line with a slope of {{{4}}} which goes through the point ({{{-1}}},{{{-3}}}) is:


{{{y=4x+1}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=4}}} and the y-intercept is {{{b=1}}}


Notice if we graph the equation {{{y=4x+1}}} and plot the point ({{{-1}}},{{{-3}}}),  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, -12, 6,
graph(500, 500, -10, 8, -12, 6,(4)x+1),
circle(-1,-3,0.12),
circle(-1,-3,0.12+0.03)
) }}} Graph of {{{y=4x+1}}} through the point ({{{-1}}},{{{-3}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{4}}} and goes through the point ({{{-1}}},{{{-3}}}), this verifies our answer.