#2color(blue)x+color(red)y=6#

The #x# intercept is the point where the line crosses the #x# axis.

#y=0# everywhere on the #x# axis.

To find the #x# intercept, substitute #color(red)y=color(red)0# into the equation and solve for #color(blue)x#.

#2color(blue)x+color(red)0=6#

#2color(blue)x=6#

#(2color(blue)x)/2 =6/2color(white)(aaa)#Divide both sides by 2

#color(blue)x=3#

The #x# intercept is then #(3,0)#.

The #y# intercept is the point where the line crosses the #y# axis.

#x=0# everywhere on the #y# axis.

To find the #y# intercept, substitute #color(blue)x =color(blue)0# into the equation and solve for #color(red)y#.

#2(color(blue)0)+color(red)y=6#

#color(red)y=6#.

The #y# intercept is then #(0,6)#.