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?

caritatsjq

caritatsjq

Answered question

2022-10-18

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 & Explanation

Kyle Delacruz

Kyle Delacruz

Beginner2022-10-19Added 21 answers

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=mx+b
Where m is the slope and b is the y-intercept value.
Substituting the slope we calculated and the y-intercept from the problem gives:
y = - 1 3 x + 2

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