Question 174263
I'll do the first two to get you started


# 1




<h4>x-intercept</h4>

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{6x-4y=12}}} Start with the given equation.



{{{6x-4(0)=12}}} Plug in {{{y=0}}}.



{{{6x-0=12}}} Multiply {{{-4}}} and 0 to get 0.



{{{6x=12}}} Simplify.



{{{x=(12)/(6)}}} Divide both sides by {{{6}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(2,0\right)].



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<h4>y-intercept</h4>

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{6x-4y=12}}} Start with the given equation.



{{{6(0)-4y=12}}} Plug in {{{x=0}}}.



{{{0-4y=12}}} Multiply {{{6}}} and 0 to get 0.



{{{-4y=12}}} Simplify.



{{{y=(12)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=-3}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-3\right)].




<hr>



# 2





If you want to find the equation of line with a given a slope of {{{-3}}} which goes through the point ({{{0}}},{{{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)(x-0)}}} Plug in {{{m=-3}}}, {{{x[1]=0}}}, and {{{y[1]=2}}} (these values are given)



{{{y-2=-3x+(-3)(-0)}}} Distribute {{{-3}}}


{{{y-2=-3x+0}}} Multiply {{{-3}}} and {{{-0}}} to get {{{0}}}


{{{y=-3x+0+2}}} Add 2 to  both sides to isolate y


{{{y=-3x+2}}} Combine like terms {{{0}}} and {{{2}}} to get {{{2}}} 

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Answer:



So the equation of the line with a slope of {{{-3}}} which goes through the point ({{{0}}},{{{2}}}) is:


{{{y=-3x+2}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=-3}}} and the y-intercept is {{{b=2}}}


Notice if we graph the equation {{{y=-3x+2}}} and plot the point ({{{0}}},{{{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, -9, 9, -7, 11,
graph(500, 500, -9, 9, -7, 11,(-3)x+2),
circle(0,2,0.12),
circle(0,2,0.12+0.03)
) }}} Graph of {{{y=-3x+2}}} through the point ({{{0}}},{{{2}}})

and we can see that the point lies on the line. Since we know the equation has a slope of {{{-3}}} and goes through the point ({{{0}}},{{{2}}}), this verifies our answer.