Question 181882


{{{5x + 3y =9}}} Start with the given equation.



{{{3y=-5x+9}}} Rearrange the terms.



{{{y=(-5x+9)/(3)}}} Divide both sides by {{{3}}} to isolate y.



{{{y=((-5)/(3))x+(9)/(3)}}} Break up the fraction.



{{{y=-(5/3)x+3}}} Reduce.



We can see that the equation {{{y=-(5/3)x+3}}} has a slope {{{m=-5/3}}} and a y-intercept {{{b=3}}}.



Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is {{{m=-5/3}}}.

Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope {{{m=-5/3}}}  and the coordinates of the given point *[Tex \LARGE \left\(-2,-1\right\)].



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



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



{{{y--1=(-5/3)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y+1=(-5/3)(x+2)}}} Rewrite {{{y--1}}} as {{{y+1}}}



{{{3(y+1)=-5(x+2)}}} Multiply both sides by 3.



{{{3y+3=-5x-10}}} Distribute



{{{3y+3+5x=-10}}} Add 5x to both sides.



{{{3y+5x=-10-3}}} Subtract 3 from both sides.



{{{5x+3y=-13}}} Combine and rearrange the terms.




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Answer:


So the equation of the line that is parallel to {{{5x + 3y =9}}} and that goes through (-2,-1) is: {{{5x+3y=-13}}} 



Also, the equation is in standard form {{{Ax+By=C}}} where {{{A=5}}}, {{{B=3}}}, and {{{C=-13}}}