A line passes through #(2 ,8 )# and #( 1, 5 )#. A second line passes through #( 6, 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 #(2  ,8 )# and #(  1,  5  )#.  A second line passes through #(  6,  8  )#.  What is one other point that the second line may pass through if it is parallel to the first line?

Savannah Aguilar · Accepted Answer

#color(green)(""(5,5))#

#(6,8)# is #4# units to the right of #(2,8)# #4# units to the right of #(1,5)# would be #(1+4,5)=(5,5)#

We could verify that these pairs form parallel lines by checking that their slopes are equal.

#"Slope " (2,8):(1,5) = (8-5)/(2-1)=3#

#"Slope " (6,8):(5,5) = (8-5)/(6-5)=3#

Caroline Aucoin · Answer

undefined If the second line is parallel to the first line, it means that their slopes are equal.

To find the slope of the first line, we use the formula:

$$ \text{Slope} = \frac{{\text{change in }} y}{{\text{change in }} x} $$

Given the points (2, 8) and (1, 5) on the first line:

$$ \text{Change in } y = 8 - 5 = 3 $$
$$ \text{Change in } x = 2 - 1 = 1 $$

$$ \text{Slope of the first line} = \frac{3}{1} = 3 $$

Since the second line is parallel to the first line, it must also have a slope of 3.

Given a point on the second line as (6, 8), we can find another point on the second line by moving 1 unit to the right and 3 units up (since the slope is 3):

$$ x = 6 + 1 = 7 $$
$$ y = 8 + 3 = 11 $$

So, another point that the second line may pass through is (7, 11).