Question

What is the slope of the line perpendicular to `y=-13/2x-5`?

Answer 1

See a solution process below:

Explanation:

The equation for the line in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(-13/2)x - color(blue)(5)`

Therefore the slope of this line is: `color(red)(m = -13/2)`

Let's call the slope of a perpendicular line: `color(blue)(m_p)`

The slope of a line perpendicular to a line with slope `color(red)(m)` is the negative inverse, or:

`color(blue)(m_p) = -1/color(red)(m)`

Substituting the slope for the line in the problem gives:

`color(blue)(m_p) = (-1)/color(red)(-13/2) = 2/13`