Answer:
[tex]\large\boxed{D.\ -\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ ||\ k\iff m_2=m_1\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------\\\\\text{We have the slope of given line a:}\ m_1=3.\ \text{Therefore the slope of a line b}\\\text{perpendicular to a is: }\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{3}[/tex]
The slope of line b is -1/3 if lines a and b are perpendicular. If the slope of line a is 3 option (D) is correct.
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
As we know if the two lines are perpendicular then the product of the slopes of these lines is equal to -1
The slope of line a is 3
The slope of line b is x(let's say)
3b = -1
b = -1/3
Thus, the slope of line b is -1/3 if lines a and b are perpendicular. If the slope of line a is 3 option (D) is correct.
Learn more about the slope of the straight line here:
brainly.com/question/3493733
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