Question 321318
# 1


{{{4x-2y=6}}} Start with the given equation.



{{{-2y=6-4x}}} Subtract {{{4x}}} from both sides.



{{{-2y=-4x+6}}} Rearrange the terms.



{{{y=(-4x+6)/(-2)}}} Divide both sides by {{{-2}}} to isolate y.



{{{y=((-4)/(-2))x+(6)/(-2)}}} Break up the fraction.



{{{y=2x-3}}} Reduce.



So the equation {{{y=2x-3}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=2}}} and the y-intercept is {{{b=-3}}} note: the y-intercept is the point *[Tex \LARGE \left(0,-3\right)]



So the slope is 2 (instead of -2)


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# 2


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,3\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=3}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-5,6\right)].  So this means that {{{x[2]=-5}}} and {{{y[2]=6}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(6-3)/(-5--2)}}} Plug in {{{y[2]=6}}}, {{{y[1]=3}}}, {{{x[2]=-5}}}, and {{{x[1]=-2}}}



{{{m=(3)/(-5--2)}}} Subtract {{{3}}} from {{{6}}} to get {{{3}}}



{{{m=(3)/(-3)}}} Subtract {{{-2}}} from {{{-5}}} to get {{{-3}}}



{{{m=-1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(-5,6\right)] is {{{m=-1}}}