Question

What is the equation of a line

that is perpendicular to the line
y = 2x + 1 and passes through the
point (4, 6)?
А y=-2x+6
B y = 2x + 6
c y=-3x+8
D y = 2x + 8

Answer 1

`y =-(1)/(2)x + 8`

Explanation:

Given

Perpendicular to
`y = 2x + 1`

Pass through
`(4,6)`

Required

Determine the line equation

First, we need to determine the slope of
`y = 2x + 1`

An equation is of the form:

`y = mx + b`

Where

`m = slope`

In this case:

`m =2`

Next, we determine the slope of the second line.

Since both lines are perpendicular, the second line has a slope of:

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

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

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

Since this line passes through (4,6); The equation is calculated as thus:

`y - y_1 = m_1(x - x_1)`

Where

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

This gives:

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

Open bracket

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

Add 6 to both sides

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

`y =-(1)/(2)x + 8`