Question

(04.02 MC)

4
What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)?

Answer 1

The intercept of the line perpendicular to the line
`y = x + 1` is 5.

Explanation:

The line
`y = x + 1` has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:

`m_(\perp) = -(1)/(m)` (1)

Where:

`m` - Slope of the original line.

`m_(\perp)` - Slope of the line perpendicular to the original line.

If we know that
`m = 1`, then the new slope is:

`m_(\perp) = -(1)/(1)`

`m_(\perp) = -1`

A line is defined by the following expression:

`y = m\cdot x + b` (2)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`m` - Slope.

`b` - Intercept.

If we know that
`(x,y) = (4,1)` and
`m = -1`, then the intercept of the line perpendicular to the original line:

`b = y - m\cdot x`

`b = 1+4`

`b = 5`

The intercept of the line perpendicular to the line
`y = x + 1` is 5.