How do you write an equation in standard form given point (3,3) and (1,-3)?
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, are integers.
#"express the equation initially in "color(blue)"slope-intercept form"#
#• y=mx+b# #"where m represents the slope and b the y-intercept.
#"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)|)))#
# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#
#"the points are " (x_1,y_1)=(3,3),(x_2,y_2)=(1-3)#
#rArrm=(-3-3)/(1-3)=(-6)/(-2)=3#
#rArry=3x+blarr" is the partial equation"#
#"to find b substitute either of the 2 points into the"#
#"partial equation"#
#"using " (3,3)#
#3=9+brArrb=-6#
#rArry=3x-6larrcolor(red)" in [slope-intercept form](https://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope-intercept-form)"#
#"rearrange equation into standard form"#
#rArr3x-y=6larrcolor(red)" in standard form"#
