Answer:
C. [tex]y=\frac{1}{3}x+4[/tex]
Step-by-step explanation:
We are given the path, [tex]y=-3x-6[/tex].
The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.
Thus, the slope of the given line is -3.
As, we have that the new path is perpendicular to the given path.
And, we know that, 'Product of slopes of perpendicular lines is -1'.
So, we get,
[tex]m\times (-3)=-1[/tex]
i.e. [tex]m=\frac{1}{3}[/tex].
Since, the new path passes through the point (-3,3). Substituting the values in the general form, we get,
[tex]3=\frac{1}{3}\times (-3)+b[/tex]
i.e. [tex]3=-1+b[/tex]
i.e. b= 3+1
i.e. b= 4.
Hence, the equation representing the new path is [tex]y=\frac{1}{3}x+4[/tex].
Thus, option C is correct.
