How do you write an equation in point-slope form for the given y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1?

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Answer 1 · 2015-08-30T16:25:27

#y = 1/3x + 5#

Given Line
Red line represents this line - y = -3 +1

Blue line is the required line. This line is vertical to y = -3 +1 and passing through the point (0, 5)

Since the two lines are vertical, the product of their slopes is equal to - 1

#m_1 xx m_2 = - 1#
#m_1# is the slope of the given line(Red line)
#m_2# is the slope of the required line (blue)

# -3 xx m_2 = -1#
# m_2 = (-1)/(-3) = 1/3#

#y - y_1 = m_2(x - x_2)#
#y - 5 = 1/3 (x- 0)#

The equation of the line is -
#y = 1/3x + 5#

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