Respuesta :
Answer:
-1/3
Explanation:
Given the line:
[tex]y=3x+4[/tex]Comparing it with the slope-intercept form [y=mx+b], the slope of the line y=3x+4:
[tex]m=3[/tex]Definition: Two lines are perpendicular if the product of their slopes is -1.
Let the slope of the new perpendicular line = n.
[tex]\begin{gathered} \implies m\times n=-1 \\ 3\times n=-1 \\ n=-\frac{1}{3} \end{gathered}[/tex]The slope of a line that is perpendicular to the given equation is -1/3.
Note
It does not matter the point it goes through. Any line perpendicular to y=3x+4 will always have a slope of -1/3.
