A line passes through #(4 ,9 )# and #(5 ,6 )#. A second line passes through #(1 ,8 )#. 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 30, 2017

#(2,5)#

Explanation:

#"one way is to establish the equation of the line passing"#
#"through "(1,8)" and evaluate for particular values of x"#

#• " parallel lines have equal slopes"#

#"to calculate the slope (m) use 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)=(4,9)" and "(x_2,y_2)=(5,6)#

#rArrm=(6-9)/(5-4)=-3#

#rArry=-3x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(1,8)" into the partial equation"#

#8=-3+brArrb=11#

#rArry=-3x+11larrcolor(red)"in slope-intercept form"#

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

#x=2toy=-6+11=5#

#rArr(2,5)" is a point on the second line"#

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