Question

Find the equation of the line through (0,4) perpendicular to the line y = 3x

Answer 1

`y = - (1)/(3) x + 4`

Explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

The product of the gradients of perpendicular lines is -1.

Gradient of given line= 3.

(Gradient of line)(3)= -1

3m= -1

m=
`- (1)/(3)`

subst. m=
`- (1)/(3)` into the equation:

`y = - (1)/(3) x + c`

To find the value of c, substitute a coordinate.

When x=0, y=4,

`4 = - (1)/( 3) (0) + c \\ 4 = c \\ c = 4`

Thus the equation of the line is
`y = -(1)/(3) x + 4`.