Question

Find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3). express answer in standard form

Answer 1

Final answer is
`x-6y=23`

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

`(1)/(6)x+(5)/(6)=y`

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:

`y-y_1=m\left(x-x_1\right)`

`y-(-3)=(1)/(6)\left(x-5\right)`

`y+3=(1)/(6)x-(5)/(6)`

`y=(1)/(6)x-(5)/(6)-3`

`y=(1)/(6)x-(23)/(6)`

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
`x-6y=23`