The slope of the line through #(5,3)# and #(2,1)# is
#color(white)("XXX")color(green)(m)=(Deltay)/(Deltax)=(3-1)/(5-2)=color(green)(2/3)#
Slope-Point Form: #color(black)((y-color(blue)(b))=color(green)(m)(x-color(red)(a))#
Using #(color(red)(a),color(blue)(b))=(color(red)(5),color(blue)(3))#
#color(white)("XXX")y-color(blue)3 = color(green)(2/3)(x-color(red)5)#
Slope-Intercept Form: #color(black)(y=color(green)(m)x+color(magenta)(k))#
Starting from the slope-point form:
#color(white)("XXX")y-3=2/3x-10/3#
#color(white)("XXX")y=color(green)(2/3)x-10/3+3#
#color(white)("XXX")y=color(green)(2/3)x+color(magenta)(""(-1/3))#
Standard Form: #color(brown)Ax+color(orange)By=color(cyan)C#
Starting from the slope-intercept form:
#color(white)("XXX")3y=2x-1#
#color(white)("XXX")color(brown)2xcolor(orange)(-3)y=color(cyan)1#
