Question 187172
{{{4x-5y=13}}} Start with the given equation.



{{{-5y=13-4x}}} Subtract {{{4x}}} from both sides.



{{{-5y=-4x+13}}} Rearrange the terms.



{{{y=(-4x+13)/(-5)}}} Divide both sides by {{{-5}}} to isolate y.



{{{y=((-4)/(-5))x+(13)/(-5)}}} Break up the fraction.



{{{y=(4/5)x-13/5}}} Reduce.



We can see that the equation {{{y=(4/5)x-13/5}}} has a slope {{{m=4/5}}} and a y-intercept {{{b=-13/5}}}.



Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is {{{m=4/5}}}.

Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope {{{m=4/5}}}  and the coordinates of the given point *[Tex \LARGE \left\(-2,-5\right\)].



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



{{{y--5=(4/5)(x--2)}}} Plug in {{{m=4/5}}}, {{{x[1]=-2}}}, and {{{y[1]=-5}}}



{{{y--5=(4/5)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y+5=(4/5)(x+2)}}} Rewrite {{{y--5}}} as {{{y+5}}}



{{{y+5=(4/5)x+(4/5)(2)}}} Distribute



{{{y+5=(4/5)x+8/5}}} Multiply



{{{y=(4/5)x+8/5-5}}} Subtract 5 from both sides. 



{{{y=(4/5)x-17/5}}} Combine like terms. 



So the equation of the line parallel to {{{4x-5y=13}}} that goes through the point *[Tex \LARGE \left\(-2,-5\right\)] is {{{y=(4/5)x-17/5}}}.