Answer:
Step-by-step explanation:
The slope of a line perpendicular to another line is the opposite reciprocal of the slope of the other line, meaning if the slope of the other line is [tex]-\frac{1}{3}[/tex], then the slope of the line perpendicular is [tex]3[/tex].
Knowing this, we can start to construct the equation for the line:
[tex]y = mx + b[/tex]
[tex]y = 3x + b[/tex]
To solve for [tex]b[/tex], we plug in the coordinates of the point that we know the line runs through, [tex](2, 1)[/tex]:
[tex]y = 3x + b[/tex]
[tex]1 = 3(2) + b[/tex]
[tex]1 = 6 + b[/tex]
[tex]b = -5[/tex]
Therefore, the slope of the line that is perpendicular ot the line provided in the equation is the following:
[tex]y = 3x - 5[/tex]
