A line passes through #(3 ,6 )# and #(4 ,8 )#. A second line passes through #(7 ,9 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Jim G.
Oct 28, 2017

#(1,-3)#

Explanation:

#"one way is to establish the equation of the line passing"#
#"through "(7,9)" and find points that lie on it"#

#• " parallel lines have equal slopes"#

#"find the slope (m) using the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(3,6)" and "(x_2,y_2)=(4,8)#

#rArrm=(8-6)/(4-3)=2#

#"the equation of the line through "(7,9)#

#y=2x+blarrcolor(blue)"slope-intercept form"#

#"to find b substitute "(7,9)" into the equation"#

#9=14+brArrb=-5#

#rArry=2x-5larrcolor(blue)"equation of line"#

#"choosing any value for x and evaluate for y"#

#x=1toy=2-5=-3#

#rArr(1,-3)" is a point on the second line"#

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