Question

What is the equation of a line perpendicular to the line `2x+y=8` and with the same y-intercept as the line `4y=x+3`?

Answer 1

`2x-4y+3=0.`

Explanation:

Call line `L_1 :2x+y=8, L_2:4y=x+3,` & reqd. line `L.`

The slope `m` of `L_1,` written as `:y=-2x+8,` is `m=-2.`

Hence, slope `m'` of `L,` `L` being perp. to `L_1,` is `m'=-1/m=1/2.`

Y-intercept `c` of `L_2,` written as `:y=1/4x+3/4,` is `c=3/4.`

Using `m'` & `c` for `L`, we get `L : y=m'x+c,` i.e., `y=1/2x+3/4.`

Writing `L` in std. form, `L : 2x-4y+3=0.`