Question

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

Answer 1

Answer:

$y = - \frac{1}{3} x + 4$

Step-by-step 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= $- \frac{1}{3}$

subst. m= $- \frac{1}{3}$ into the equation:

$y = - \frac{1}{3} x + c$

To find the value of c, substitute a coordinate.

When x=0, y=4,

$4 = - \frac{1}{ 3} (0) + c \\ 4 = c \\ c = 4$

Thus the equation of the line is $y = -\frac{1}{3} x + 4$.