A line passes through #(2 ,8 )# and #(3 ,9 )#. A second line passes through #(7 ,4 )#. 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 · 2018-06-10T20:50:07

#color(blue)((0,-3)#

First find the gradient of the line passing through points #(2,8)# and #(3,9)#

#(9-8)/(3-2)=1#

Any line parallel to this will have the same gradient.

Equation of the line passing through point #(7,4)#.

Using point slope form of a line:

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

Where #m# is the gradient:

#y-4=(x-7)#

#y=x-3#

To find another point that this line passes through, we just put in a value for #bbx# and calculate the corresponding value of #bby#:

Let #x=0#

Then:

#y=0-3=-3#

Another point is #(0,-3)#

The co-ordinates of a point on this line could be written:

#(x, x-3)#

PLOT:

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