A line passes through (2, -1) and (8, 4). How do you write an equation for the line in point-slope form Rewrite the equation in standard form using integers?

1 Answer
Apr 30, 2018

#y-4=5/6(x-8)" and "5x-6y=24#

Explanation:

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

#•color(white)(x)y-y_1=m(x-x_1)#

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

#"to calculate m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(2,-1)" and "(x_2,y_2)=(8,4)#

#rArrm=(4-(-1))/(8-2)=5/6#

#"using "(8,4)" as point on line then"#

#y-4=5/6(x-8)larrcolor(red)"in point-slope form"#

#"the equation of a line in "color(blue)"standard form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#

#"where A is a positive integer and B, C are integers"#

#rArry-4=5/6x-20/3#

#"multiply all terms by "6#

#rArr6y-24=5x-40#

#rArr5x-6y=24larrcolor(red)"in standard form"#