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

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Answer:

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.

User Fong Kah Chun
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