Question

Determine the equation of the line that passes through the point (1/9,−3) and is parallel to the line −8y+4x=4.

Answer 1

Given:

The point lies on the line is (1/9, -3).

The parallel line is -8y+4x=4.

Required:

We need to find the equation of the line.

Step-by-step explanation:

Consider the parallel line.

`-8y+4x=4`

Subtract 4x from both sides.

`-8y+4x-4x=4-4x`
`-8y=4-4x`

Divide both sides by (-8).

`-(8y)/(-8)=(4)/(-8)-(4x)/(-8)`
`y=-(1)/(2)+(1)/(2)x`
`y=(1)/(2)x-(1)/(2)`

Which is of the form

`y=mx+b`

where slope,m=1/2.

We know that the slope of the parallel lines is the same.

The slope of the required line is m =1/2.

Consider the line equation.

`y=mx+b`

Substitute x =1/9, y=-3, and m=1/2 in the equation to find the value of b.

`-3=(1)/(9)((1)/(2))+b`
`-3=(1)/(18)+b`

Subtract 1/18 from both sides.

`-3-(1)/(18)=(1)/(18)+b-(1)/(18)`
`-3*(18)/(18)-(1)/(18)=b`
`(-54-1)/(18)=b`
`b=-(55)/(18)`

Substitute m=1/2 and b =-55/18 in the line equation.

`y=(1)/(2)x-(55)/(18)`

Multiply both sides by 18.

`18y=18*(1)/(2)x-18*(55)/(18)`
`18y=19x-55`

Final answer:

`18y=19x-55`