A line passes through #(2 ,8 )# and #( 7, 2 )#. A second line passes through #( 6, 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 #(2  ,8 )# and #(  7,  2  )#.  A second line passes through #(  6,  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 on Line CD is #color(green)(1,7)#

Slope of AB = Slope of CD =#m = (2-8) / (7-2) = -6/5#

Equation of line CD is

#y - 1 = -(6/5) (x - 6)#

#5y - 5 = -6x + 36#

#5y + 6x = 41#

Let x = 1. Then y = (41 - 6)/5 = 7#

Mason Adams · Answer

undefined Since the second line is parallel to the first line, it will have the same slope as the first line. To find the slope of the first line, use the formula:

slope = (change in y) / (change in x)

For the first line, between points (2, 8) and (7, 2):
slope = (2 - 8) / (7 - 2) = -6 / 5

Now, apply this slope to the point (6, 1) to find a point on the second line:
Using the slope-intercept form of a line, which is y = mx + b, where m is the slope:
1 = (-6/5)(6) + b
1 = -36/5 + b
b = 1 + 36/5
b = 41/5

So, the equation of the second line is y = (-6/5)x + 41/5.

Now, to find another point on this line, choose any value for x and solve for y. For simplicity, let's choose x = 0:
y = (-6/5)(0) + 41/5
y = 41/5

Therefore, another point on the second line is (0, 41/5).