A line passes through #(4 ,9 )# and #(7 ,4 )#. A second line passes through #(8 ,7 )#. 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 · 2016-08-07T13:51:52

#y=-5/3x+61/3#

As the two lines are parallel they both have the same gradient.

gradient (slope) #->("change in the y-axis")/("change in the x-axis")#

Let point 1 be #P_1->(x_1,y_1)=(4,9)#
Let point 2 be #P_2->(x_2,y_2)=(7,4)#

Let point 3 be #P_3->(x_3,y_3) =(8,7)#

For the first line reading left to right #->x_1 to x_2#

So gradient is #P_2-P_1 ->(y_2-y_1)/(x_2-x_1) = (4-9)/(7-4) =-5/3#

Thus the gradient is # m=-5/3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus equation for the second line #-> y=-5/3x+c#

This passes through the point #P_3 ->(x_3,y_3) =(8,7)#

#=> y_3=-5/3x_3+c" "->" "7=-5/3(8)+c#

#=>c=7+5/3(8) = 61/3#

Thus the equation of the second line is:

#y=-5/3x+61/3#