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#