A line passes through #(3 ,2 )# and #(7 ,3 )#. A second line passes through #(1 , 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2018-05-19T08:06:17

One other point on the second line is #color(maroon)(5,2)#

Slope of a line #m = (y_2-y_1)/ (x_2-x_1)#

Slope of first line #m_1 = (3-2)/(7-3) = 1/4#

Since second line is parallel to the first line, their slopes are equal.

Therefore slope of second line #m_2 = m_1 = 1/4#

Equation of second line is given by point - slope formula

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

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

#4y -4 = x - 1#

#x - 4y = -3#

When #y = 2, x = 4*2 - 3 = 5#