If you have two ponts, (-2,-4) and (10,6), how do you calculate the line that goes through these ponts in the form of Ax+By=C?

1 Answer
Jim G.
May 12, 2018

#5x-6y=14#

Explanation:

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

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

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

#"we will require to obtain the equation in some other"#
#"form to begin with and rearrange into standard form"#

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

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"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,-4)" and "(x_2,y_2)=(10,6)#

#rArrm=(6-(-4))/(10-(-2))=10/12=5/6#

#rArry=5/6x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into"#
#"the partial equation"#

#"using "(10,6)" then"#

#6=25/3+brArrb=18/3-25/3=-7/3#

#rArry=5/6x-7/3larrcolor(red)"in slope-intercept form"#

#"multiply all terms by 6"#

#rArr6y=5x-14#

#rArr5x-6y=14larrcolor(red)"in standard form"#

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