A line passes through #(0 ,5 )# and #(8 ,3 )#. A second line passes through #(7 ,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 #(0    ,5  )# and #(8   ,3   )#.  A second line passes through #(7   ,1  )#.  What is one other point that the second line may pass through if it is parallel to the first line?

Sophia Alfred · Accepted Answer

One such point is #(11,0)#

Let this point be #(a,b)#.

As the slope of line joining #(0,5)# and #(8,3)# is

#(3-5)/(8-0)=-2/8=-1/4#

and the slope of line joining #(7,1)# and #(a,b)# should also be the same i.e.

#(b-1)/(a-7)=-1/4#

or #4b-4=-a+7#

or #a=11-4b#

Hence any line joining a point #(11-4b,b)# with #(7,1)# will be parallel to line joining #(0,5)# and #(8,3)#

Let #b=0#, then the point is #(11,0)#

graph{(x+4y-20)(x+4y-11)=0 [-8, 12, -0.8, 9.2]}

Aaliyah Anderson · Answer

undefined To find a point that the second line may pass through if it is parallel to the first line, you can use the slope-intercept form of a line. Since the second line is parallel to the first, it will have the same slope.

1. First, find the slope of the first line using the points (0, 5) and (8, 3).
2. Then, using the slope found, and the given point (7, 1), use the point-slope form of a line to find the equation of the second line.
3. Solve the equation to find the value of the second point on the line.