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

##### 1 Answer

#### 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"#