Question

Write the equation of a line that is perpendicular to x=3x=3x, equals, 3 and that passes through the point (0,-4)(0,−4)left parenthesis, 0, comma, minus, 4, right parenthesis.

Answer 1

Answer: $x+3y=12$

Step-by-step explanation:

Slope of two lines that are perpendicular to each other is 1.

If one line is $y=3x$, then its slope = 3   [by comparing to the linear equation y= mx+c, here m=3]

Let n be the slope of the required line, then

$n\times3=-1\\\\\rightarrow\ n=\dfrac{-1}{3}$

Equation of line with slope n and passers through (a,b) is

$(y-b)=n(x-a)$

Equation of line with slope n= $\dfrac{-1}{3}$ and passes through point ( 0,-4) :

$(y-(-4))=\dfrac{-1}{3}(x-0)\\\\\Rightarrow\ y+4=\dfrac{-1}{3}x\\\\\Rightarrow\ -3(y+4)=x\\\\\Rightarrow-3y-12=x\\\\\Rightarrow x+3y=12$

Hence, Required equation : $x+3y=12$