A line passes through #(2 ,8 )# and #( 7, 5 )#. 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?

2 Answers
Lil Del
Oct 5, 2016

#(11, -2)# is a point through which the second line might pass.

Explanation:

Parallel lines have equal slopes, so the first step is to find the slope of the line which passes through (#2, 8)# and #(7, 5)# using the slope formula. The formula for slope, #m#, is:
#m = (y_2 - y_1)/(x_2 - x_1)#

Substitute the known coordinates:
#m = (5 -8)/(7 - 2)#
#m = (-3)/5#

Remember that slope is "rise over run", so the numerator of the slope can be added to the #y#-coordinate of the known point and the denominator of the slope can be added to the #x#-coordinate of the known point to find another point on the other line.

#(6 + 5, 1 + -3)#
#(11, -2)#

So, #(11, -2)# is a point through which the second line might pass.

Alan P.
Oct 5, 2016

#color(green)(""(11,-2))#

Explanation:

Slope of line through #(2,8)# and #(7,5)#
#color(white)("XXX")m=(Deltay)/(Deltax)= (8-5)/(2-7)=-3/5#

This means that a change #Deltax=5# would correspond to a change #Deltay=-3#

So #(6+Deltax,1+Deltay)# would be a point #(11,-2)#

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