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
