Question

Line p is represented by the equation 2x-y=-5. If line r passes through the point (6,4) and is perpendicular to line p, what is the equation of line r?

Answer 1

`y = -(1)/(2)x + 7`

Explanation:

Given

`2x - y = 5`

`Point = (6,4)`

Required

Determine the equation of perpendicular line, r

First we need to determine the slope of the given equation

`2x - y = 5`

Make y the subject:

`y = 2x - 5`

The general form of an equation is:

`y = mx + b`

Where:

`m = slope`

By comparison;

`m = 2`

Since both lines are perpendicular:

We have:

`m_1 = -1/m` to calculate the slope of the perpendicular line

`m_1 = -(1)/(2)`

Equation of the line can be solved using:

`y - y_1 = m(x - x_1)`

Where

`(x_1,y_1) = (6,4)`

`m = m_1 = -(1)/(2)`

So: the equation becomes

`y - 4 = -(1)/(2)(x - 6)`

`y - 4 = -(1)/(2)x + 3`

Solve for y

`y = -(1)/(2)x + 3 + 4`

`y = -(1)/(2)x + 7`

Hence:

The required equation is

`y = -(1)/(2)x + 7`