Answer:
Step-by-step explanation:
If a line has a slope of [tex]3[/tex], then the line perpendicular to it has a slope of [tex]-\frac{1}{3}[/tex] (opposite reciprocal).
With this, we can construct a line in slope-intercept form:
[tex]y = mx + b[/tex]
Where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept.
We already know the slope of the line, so we can plug it into the equation:
[tex]y = -\frac{1}{3}x + b[/tex]
We also know that the line passes through the point [tex](-8, -2)[/tex], so we can plug this into the equation to get [tex]b[/tex]:
[tex]-2 = -\frac{1}{3}(-8) + b[/tex]
[tex]-2 = \frac{8}{3} + b[/tex]
[tex]b = -\frac{14}{3}[/tex]
