A line passes through #(1 ,4 )# and #(7 ,4 )#. 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 #(1    ,4  )# and #(7   ,4   )#.  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?

Avery Allen · Accepted Answer

One other point is (2,1) passing through point (8,1) and parallel to the first line.

Parallel lines have same slope

Slope of first line #m_f = (4-4) / (7-6) = 0#

Equation of second line passing through point (8,1) and parallel to first line is

#y - 1 = 0 * (x - 8) = 0#

Therefore #y = 1# is the equation.

‘For #x = 2#, y will remain as 1.

One other point is (2,1) passing through point (8,1) and parallel to the first line.

Sadie Allen · Answer

undefined To find a point that the second line may pass through if it is parallel to the first line, we need to use the slope of the first line, which is (4 - 4) / (7 - 1) = 0. The second line needs to have the same slope since parallel lines have equal slopes. Therefore, for the second line, the slope should also be 0. To find another point, we can use the given point (8, 1) and adjust its y-coordinate while keeping the x-coordinate the same. Since the slope is 0, the y-coordinate remains the same. Thus, the second line may pass through the point (8, 4).