Answer:
[tex]y = - \frac{1}{3} x + 4[/tex]
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= [tex] - \frac{1}{3} [/tex]
subst. m= [tex] - \frac{1}{3} [/tex] into the equation:
[tex]y = - \frac{1}{3} x + c[/tex]
To find the value of c, substitute a coordinate.
When x=0, y=4,
[tex]4 = - \frac{1}{ 3} (0) + c \\ 4 = c \\ c = 4[/tex]
Thus the equation of the line is [tex]y = -\frac{1}{3} x + 4[/tex].
