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chudung1976
You know two lines y=ax+b and y=mx+n that are perpendicular, so we have the product a*m=-1

+ This line is perpendicular to y=13x-5, so it has equation: y=-1/13x+b
+ And it passes through the point (3;1), so we have x=3, y=1. So 1=-1/13 *3+b
and b= 1+3/13= 16/13
And we have y=-1/13x+16/13
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The slope of a line perpendicular to another is (-1) multiplied by the

reciprocal of the slope of the other line.

  • The equation of the line is; 13·y = 16 - x

Reasons:

The equation of the given line is; y = 13·x - 5

The point through which the perpendicular line passes = P(3, 1)

Solution:

The slope of a line, b, perpendicular to a line a with slope m is [tex]\displaystyle \mathbf{-\frac{1}{m}}[/tex]

The equation of the given line, y = 13·x - 5, is given in slope and intercept form, y = m·x + c

Therefore, the slope, m = 13

The slope of the perpendicular line in therefore, [tex]\displaystyle \mathbf{-\frac{1}{13}}[/tex]

Which gives the equation of the perpendicular line in point and slope form as follows;

[tex]\displaystyle y - 1 = \mathbf{ -\frac{1}{13} \times (x - 3)}[/tex]

13·y - 13 = 3 - x

13·y = 3 - x + 13 = 16 - x

The equation of the line is 13·y = 16 - x

Learn more about the equation of a line perpendicular to another line here:

https://brainly.com/question/2141803