Question 236694


{{{3x-2y=8}}} Start with the given equation.



{{{-2y=8-3x}}} Subtract {{{3x}}} from both sides.



{{{-2y=-3x+8}}} Rearrange the terms.



{{{y=(-3x+8)/(-2)}}} Divide both sides by {{{-2}}} to isolate y.



{{{y=((-3)/(-2))x+(8)/(-2)}}} Break up the fraction.



{{{y=(3/2)x-4}}} Reduce.



We can see that the equation {{{y=(3/2)x-4}}} has a slope {{{m=3/2}}} and a y-intercept {{{b=-4}}}.



Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is {{{m=3/2}}}.

Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope {{{m=3/2}}}  and the coordinates of the given point *[Tex \LARGE \left\(-1,4\right\)].



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



{{{y-4=(3/2)(x--1)}}} Plug in {{{m=3/2}}}, {{{x[1]=-1}}}, and {{{y[1]=4}}}



{{{y-4=(3/2)(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-4=(3/2)x+(3/2)(1)}}} Distribute



{{{y-4=(3/2)x+3/2}}} Multiply



{{{y=(3/2)x+3/2+4}}} Add 4 to both sides. 



{{{y=(3/2)x+11/2}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



So the equation of the line parallel to {{{3x-2y=8}}} that goes through the point *[Tex \LARGE \left\(-1,4\right\)] is {{{y=(3/2)x+11/2}}}.



Here's a graph to visually verify our answer:

{{{drawing(500, 500, -10, 10, -10, 10,
graph(500, 500, -10, 10, -10, 10,(3/2)x-4,(3/2)x+11/2),
circle(-1,4,0.08),
circle(-1,4,0.10),
circle(-1,4,0.12))}}}


Graph of the original equation {{{y=(3/2)x-4}}} (red) and the parallel line {{{y=(3/2)x+11/2}}} (green) through the point *[Tex \LARGE \left\(-1,4\right\)].