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?

Question

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?

James Atkins · Accepted Answer

(0,4)

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)#

Theodore Abad · Answer

undefined To find a point through which the second line passes, we need to maintain the same slope as the first line, since the lines are parallel. The slope of the first line passing through (4,9) and (1,6) is (9-6)/(4-1) = 3/3 = 1. So, the second line should also have a slope of 1. Therefore, if the second line passes through (3,7), one other point it may pass through is (4,8).