"the equation of a line in "color(blue)"standard form"the equation of a line in 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"
"first, obtain the equation in "color(blue)"slope-intercept form"
•color(white)(x)y=mx+c
"where m is the slope and c 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)=(5,-2)" and "(x_2,y_2)=(-5,4)
m=(4-(-2))/(-5-5)=6/(-10)=-3/5
y=-3/5x+clarrcolor(blue)"is the partial equation"
"to find c substitute either of the 2 given points into"
"the partial equation"
"using "(5,-2)" then"
-2=-3+crArrc=-2+3=1
y=-3/5x+1larrcolor(red)"in slope-intercept form"
"multiply all terms by 5"
5y=-3x+5
"add "3x" to both sides"
3x+5y=5larrcolor(red)"in standard form"