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?

Question

1510 views around the world

You can reuse this answer
Creative Commons License

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)#

PLOT: enter image source here