#"establish the equation of the parallel line"#
#"the equation of a line in "color(blue)"slope-intercept form "# is.
#•color(white)(x)y=mx+b#
#"where m is the slope and b the y-intercept"#
#"to calculate 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)=(5,0)" and "(x_2,y_2)=(7,9)#
#rArrm=(9-0)/(7-5)=9/2#
#• " parallel lines have equal slopes"#
#rArr"slope of parallel line "=9/2#
#rArry=9/2x+b color(blue)" is the partial equation"#
#"to find b substitute "(3,6)" into the partial equation"#
#6=27/2+brArrb=-15/2#
#rArry=9/2x-15/2larrcolor(blue)"equation of parallel line"#
#"choose any value for x and substitute into the equation"#
#x=2toy=9-15/2=3/2#
#"another point on the line is "(2,3/2)#