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

1 Answer
Oct 25, 2016

(0,4)

Explanation:

First of all, both of the lines are parallel to each other, meaning they have the same slope

To find the slope, we use the slope formula:

#(y_2-y_1)/(x_2-x_1)#

Plug in the numbers from the points of the 2 lines, and find the slope of both lines

#(9-6)/(4-1) = 3/3 = 1#

The 1 is the slope of both of the lines, as parallel lines have the same slope.

Now, we can use the point-slope formula to get the slope-intercept equation of the second line

#y-y_1=m(x-x_1) #

Plug in the numbers, and get the new formula

#y-7=1(x-3)#
#y-7=x-3#
#y=x+4#

Now, we can get a second point for the second line: the y-intercept. To find the y-intercept, plug in 0 for the x value of the equation, and simplify. The resulting point found should be your new answer:

#(0,4)#