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IrinaK [193]
3 years ago
14

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

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

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.

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