A line passes through #(4 ,9 )# and #(1 ,7 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Mar 23, 2016

the slope of our first line is the ratio of change in y to change in x between the two given points of (4, 9) and (1, 7).
our second line will have the same slope because it is to be parallel to the first line.

our second line will have the form #y=2/3 x + b# where it passes through the given point (3, 6). Substitute x = 3 and y = 6 into the equation so that you can solve for the 'b' value.

you should obtain the equation of the 2nd line as:
#y=2/3 x + 4#

there are an infinite number of points you could select from that line not including the given point (3, 6) but the y intercept would be a very convenient one since it is the point (0, 4) and can be readily determined from the equation.