How do you write the equation given (6,-3) with slope 2/3?

2 Answers
Binayaka C.
May 1, 2017

Equation of the line is #2x-3y = 21 #

Explanation:

The equation of a line passing through #(x_1,y_1)# having slope #m# is #y-y_1= m(x-x_1)#.

Therefore, the equation of a line passing through #(6, -3)# having slope #2/3# is #y-(-3)= 2/3(x-6) or 3(y+3)= 2(x-6) or 2x-3y = 21#.

Equation of the line is #2x-3y = 21 # [Ans]

Jim G.
May 1, 2017

#y=2/3x-7#

Explanation:

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

#"here " m=2/3" and " (x_1,y_1)=(6,-3)#

#y-(-3)=2/3(x-6)larrcolor(red)" substitute into equation"#

#rArry+3=2/3(x-6)larrcolor(red)" in point-slope form"#

#"distribute / simplify gives an alternative version of equation"#

#y+3=2/3x-4#

#y=2/3x-4-3#

#rArry=2/3x-7larrcolor(red)" in slope-intercept form"#

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