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
Oct 28, 2017
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"#