Question

In the xy-coordinate plane, the slope of line L is 3 and its y-intercept is 2. what is the equation of the line perpendicular to L that intersects L at its y- intercept?

Answer 1

`y = color(red)(-1/3)x + color(blue)(2)`

Explanation:

First, we need to determine the slope of the line perpendicular to L. The slope of L, let's call it `m_L = 3`. The slope of a perpendicular line, let's call it `m_p` is the negative inverse of the slope of line L. Or, `m_p = -1/m_L`

`m_p = -1/3`

And, because the y-intercepts are the same we can use the slope-intercept to find the equation for the line in the problem:

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.

Substituting the slope we calculated and the y-intercept from the problem gives:

`y = color(red)(-1/3)x + color(blue)(2)`