A line passes through #(8 ,5 )# and #(2 ,1 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Steve M
Feb 20, 2017

#(0,4)# is a suitable point

Explanation:

Consider the first line passing through the points #(8,5)# and #(2,1)#

The gradient of this line is given by:

# m_1 = (Delta y)/(Delta x) = (5-1)/(8-2) 4/6 = 2/3 #

In order for the second line to be parallel to this point it must have the same gradient, So it passes through #(3,5)# and has gradient #2/3#, so we can use the point/gradient formula for a straight line #y-y_1=m(x=x1)# to give;

# y-6=2/3(x-3) #
# y-6=2/3x-2 #
# y=2/3x+4 #

We can pick any point on this line , choose

# x= 0 => y=4 #

Hence #(0,4)# is a suitable point

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