A line passes through #(6 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,8 )#. 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 #(6    ,2   )# and #(6   ,7   )#.  A second line passes through #(3    ,8  )#.  What is one other point that the second line may pass through if it is parallel to the first line?

Avery Allen · Accepted Answer

For example: #(3,7)# or all the other providing that the #x=3#.

Have a look:

Carson Arnold · Answer

undefined If the second line is parallel to the first line, then it will have the same slope as the first line. To find the slope of the first line passing through the points (6, 2) and (6, 7), we use the formula:

$$ \text{Slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Substituting the given points into the formula, we get:

$$ \text{Slope} = \frac{{7 - 2}}{{6 - 6}} = \frac{5}{0} $$

Since the denominator is 0, it indicates that the line is vertical, and its slope is undefined. Therefore, the second line must also be vertical and parallel to the first line.

For a vertical line passing through the point (3, 8), all points on this line will have an x-coordinate of 3. So, any point with an x-coordinate of 3 will lie on the second line.

Therefore, any point of the form (3, y), where y is any real number, will lie on the second line and be parallel to the first line.