A line passes through #(4 ,3 )# and #(2 ,6 )#. A second line passes through #(1 ,8 )#. 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 · 2018-06-19T14:03:26

#color(blue)((2,13/2)#

If two lines are parallel then their gradients are the same.

Gradient of line passing through points #(4,3),(2,6)#

Let #m# be the gradient:

Then:

#m=(6-3)/(2-4)=-3/2#

The line passing through point #(1,8)# also has gradient #-3/2#

Equation of this line using point slope form:

#(y_2-y_1)=m(x_2-x_1)#

#y-8=-3/2(x-1)#

#y=-3/2x+19/2#

So another point on the line passing through point #(1,8)# and parallel to the other line is any point that satisfies the equation:

#y=-3/2x+19/2#

We could express this as.

#(x,-3/2x+19/2)#

For a specific value, we could choose #x=2#

#y=-3/2(2)+19/2=13/2#

co-ordinates:

#(2,13/2)#

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