How do you write an equation in standard form given point (-3,-1) and (2,5)?

1 Answer
Mar 31, 2017

#6x-5y=-13#

Explanation:

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.

Begin by expressing the equation in #color(blue)"point-slope form"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#

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)|)))#
where # (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

The 2 points here are (-3 ,-1) and (2 ,5)

let # (x_1,y_1)=(-3,-1)" and " (x_2,y_2)=(2,5)#

#rArrm=(5-(-1))/(2-(-3))=6/5#

Either of the 2 given points can be used for # (x_1,y_1)#

#"Using "m=6/5" and " (x_1,y_1)=(2,5)# we can establish the equation.

#rArry-5=6/5(x-2)larrcolor(red)" in point-slope form"#

distribute bracket and rearrange into standard form.

#y-5=6/5x-12/5#

multiply ALL terms on both sides by 5

#rArr5y-25=6x-12#

#rArr6x-5y=-13larrcolor(red)" in standard form"#