What is the equation of the line that passes through (4,- 1) and is perpendicular to #y = -x + 1#?

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Answer 1 · 2018-02-01T02:50:04

Equation of perpendicular line is #color(red)(y - x = -5)#

Perpendicular lines will have slopes #m_a, m_b# such that

#m_a * m_b = -1#

Given equation is

#y = -x + 1# Eqn (1)

It is in the standard form of equation,

#y = mx + c# Eqn (2), where m is the slope of the equation.

Comparing the coefficients of x term in both the equations,

#m_a = -1#, slope of line A.

Slope of line B #m_b = - (1/ m_a) = -1 / -1 = 1#

Equation of the perpendicular line B passing through point (4, -1) is given by the formula,

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

#y - (-1) = m_b ( x - 4)# where #m_b = 1#

#y + 1 = 1 * ( x - 4) = x - 4#

Equation of perpendicular line B is

#color(red)(y - x = -5)#