This is a straight line equation.

#color(blue)("Using first principles method")#

Given:#" "-4x-2y=14#

Add #2y# to both sides

#14+2y=-4x#

Subtract 14 from both sides

#2y=-4x-14#

Divide both sides by 2

#y=-4/2x-14/2#

#color(blue)(y=-2x-7)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Using shortcut method")#

#color(brown)("It takes a lot more lines to explain than to do it!")#

Move #-2y# to the other side of = and change its sign

#-4x=14+2y#

Move the 14 to the other side of = and change its sign

#-4x-14=2y#

Write as:

#2y=-4x-14#

Move the 2 from #2y# to the other side of the = and change it from multiply to divide (reverse its action)

#y=-4/2 x-14/2#

#color(blue)(y=-2x-7)#..................Equation(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The intercepts are at when #x=0# and #y=0#

#color(brown)("Set "x=0" so Equation(1) becomes:")#

#y=-2(0)-7#

#y=-7 ->" "color(blue)((x,y)=(0,-7) larr" y-intercept")#

#color(brown)("Set "y=0" so Equation(1) becomes:")#

#0=-2x-7#

#+2x=-7#

#x=-7/2->" "color(blue)((x,y)=(-7/2,0)larr" x-intercept")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mark your two points and draw a straight line through them