Question

Find the equation of a line parallel to 3x+4y=12 that passes through the point (8,-2)

Answer 1

Given:

The given line equation is 3x+4y=12.

The point (8,-2).

Required:

We need to find the line equation parallel to the given equation.

Step-by-step explanation:

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

`3x+4y=12`
`Substract\text{ 3x from both sides of the equation}`
`3x+4y-3x=12-3x`
`4y=12-3x`
`4y=-3x+12`
`Divide\text{ both sides of the equation by 4.}`
`(4y)/(4)=-(3x)/(4)+(12)/(4)`
`y=-(3x)/(4)+(12)/(4)`
`y=-(3x)/(4)+3`

The given equation is of the form.

`y=mx+b`

Where the slope m=-3/4.

Consider the point-slope form

`y-y_1=m(x-x_1)`
`Substitute\text{ m=-}(3)/(4),\text{ }y_1=-2\text{ and }x_1=8\text{ in the equation.}`
`y-(-2)=-(3)/(4)(x-8)`
`y+2=-(3)/(4)(x-8)`
`y+2=-(3)/(4)x-(-(3)/(4))8`
`y+2=-(3)/(4)x-(-3)2`
`y+2=-(3)/(4)x+6`

Subtract 2 from both sides of the equation.

`y+2-2=-(3)/(4)x+6-2`
`y=-(3)/(4)x+4`

Final answer:

The equation of the parallel line is

`y=-(3)/(4)x+4`