Answer:
Final answer is [tex]x-6y=23[/tex]
Step-by-step explanation:
We need to find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3).
So first we need to find the slope of given line.
rewirite x=6y-5 in y=mx+b form
x+5=6y
[tex]\frac{1}{6}x+\frac{5}{6}=y[/tex]
Compare given equation with y=mx+b
we get: m=1/6
We know that parallel equations has equal slope.
Then slope of required line m=1/6
Now plug the given point (5,-3) and slope m=1/6 into point slope formula:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-(-3)=\frac{1}{6}\left(x-5\right)[/tex]
[tex]y+3=\frac{1}{6}x-\frac{5}{6}[/tex]
[tex]y=\frac{1}{6}x-\frac{5}{6}-3[/tex]
[tex]y=\frac{1}{6}x-\frac{23}{6}[/tex]
Now we need to rewrite that equation in standard form. Ax+By=C.
6y=x-23
x-23=6y
x-6y=23
Hence final answer is [tex]x-6y=23[/tex]
