#"we require to know that"#

#color(red)(bar(ul(|color(white)(2/2)color(black)("parallel lines have equal slope")color(white)(2/2)|)))#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#

where m represents the slope and b, the y-intercept.

#"rearrange " 4x-7y-8=0" into this form"#

#"subtract 4x from both sides"#

#cancel(4x)cancel(-4x)-7y-8=0-4x#

#rArr-7y-8=-4x#

#"add 8 to both sides"#

#-7ycancel(-8)cancel(+8)=-4x+8#

#rArr-7y=-4x+8#

#"divide ALL terms by -7"#

#(cancel(-7) y)/cancel(-7)=(-4)/(-7)x+8/(-7)#

#rArry=4/7x-8/7larr" in slope-intercept form"#

#rArr"slope "=m=4/7#

#"the equation of a line in "color(blue)"point-slope form"# is.

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

where # (x_1,y_1)" is a point on the line"#

#"using " m=4/7" and " (x_1,y_1)=(-5,4)" then"#

#y-4=4/7(x-(-5))#

#rArry-4=4/7(x+5)larrcolor(red)" in point-slope form"#