Question

Write an equation for a line parallel to: Y = 1/2x + 4 that goes through the point (3,5)

A) y - 5 = 1/2 (x - 3)
B) y - 5 = -2 (x - 3)
C) y - 3 = -2 (x - 5)
D) y - 3 = 1/2 (x - 5)

Answer 1

The equation of a line passing through the point (3 , 5) and parallel to Y = 1/2x + 4 is

A) y - 5 = 1/2 (x - 3)

Explanation:

Given:

equation of line

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

To Find:

The equation of a line passing through the point (3 , 5) and parallel to Y = 1/2x + 4

Solution:

Let A be the point A (x₁ ,y₁ ) ≡ (3 , 5)

on the required equation of a line.

As the required line is parallel slope of the line are equal.

On comparing the
`y=(1)/(2)x + 4`

equation with

`y=mx +c`

slope =m =
`(1)/(2)`

∴ slope of the required line is also m =
`(1)/(2)`

as lines parallel.

We know that equation of line having slope m and passing through point (x₁ ,y₁ )is given by

`(y-y_(1))= m(x-x_(1))`

so on substituting the above values i.e m=
`(1)/(2)` and A (x₁ ,y₁ ) ≡ (3 , 5)

we get

`y-5=(1)/(2)(x-3)`

∴
`y-5=(1)/(2)(x-3)` as per required