A line passes through #(3 ,4 )# and #(7 ,3 )#. A second line passes through #(8 , 1 )#. 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 #(3    ,4   )# and #(7    ,3   )#.  A second line passes through #(8 ,  1  )#.  What is one other point that the second line may pass through if it is parallel to the first line?

Aaliyah Anderson · Accepted Answer

The second line will pass through its y-intercept which is #(0,3)#

To solve this question, you need to find the slope of the first line from the given points on it. Then you can use the same slope (as the lines are parallel) to determine the y-intercept of the second line.

The slope formula states: #m = (rise) / (run)#

OR: #m = (y2-y1) / (x2 -x1)# We have: #(3,4) and (7,3)#

#m = (3 - 4)/(7 - 3) = (-1/4)# This is a line with a negative (falling) slope.

If we now use the given point #(8,1)#on the second line and the slope we calculated in the slope-intercept equation:

#y = mx + b#

We can write this as: #b=y-mx#

#b = 1 - (-1/4)(8)#

#b= 1+(8/4) = 3# so the other point is #(0,3)#

To check, use the given point on the second line and your new point in the slope formula or you can graph these lines easily:

#m = (rise) / (run)#

#(- 1/4) = (1-3)/(8-0)#

#(- 1/4) = -2/8 =-1/4#

Violet Aldrich · Answer

undefined One other point that the second line may pass through if it is parallel to the first line is (12, 0).