How do you graph #-3x=6y-2# using the intercepts?

Question

Ethan Adkins · Accepted Answer

Please see below.

Intercepts formed by the line #-3x=6y-2# on #x# axis and #y# axis can be obtained by putting #y=0# and #x=0# respectively in the equation #-3x=6y-2#. Doing so, intercept on #x# axis is given by #-3x=6*0-2=-2# or #x=2/3#. And intercept on #y# axis is given by #-3*0=6y-2# or #y=1/3#. Hence, intercept on #x# axis is #2/3# and that on #y# axis is #1/3#. So plotting points #(2/3,0)# and #(0,1/3)# and joining them wil give us the desired graph. graph{3x+6y-2=0 [-0.2865, 0.9635, -0.1375, 0.4875]} Additional information - Equation of a line which forms an intercept #a# on #x# axis and #b# on #y# axis is given by #x/a+y/b=1#.

Nathan Axel · Answer

Mart the points
#color(green)(=>y_("intercept")->(x,y)->(0,1/3)#
#=>color(green)(x_("intercept") ->(x,y)->(2/3,0)#
and draw a straight line through them but extend it to the edges of the graph.

We could if we so chose manipulate the given equation so that we have the standard form of #y=mx + c# and then determine the intercepts, but there is no need to. #color(green)("Determine x-intercept")# Using first principle method Knowing the First principle method comes in handy when doing higher level math. The #x"-intercept"# is when #color(blue)(y=0)# So by substitution we have: #color(brown)(-3x=6y-2" "->" "-3x=6(color(blue)(0))-2)# #=>-3x=-2# Multiply both sides by #(-1)# #=> +3x=+2# Divide both sides by 3 #3/3x=2/3# But #3/3=1# #color(green)(x_("intercept")=2/3) ->(x,y)->(2/3,0)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(green)("Determine y-intercept")# Using shortcuts method The #y"-intercept"# is when #x=0# #-3(0)=6y-2# #color(green)(=>y=+2/6=1/3)->(x,y)->(0,1/3)#

Avery Alexander · Answer

undefined To graph the equation -3x = 6y - 2 using intercepts:
1. Find the x-intercept by setting y = 0 and solving for x.
2. Find the y-intercept by setting x = 0 and solving for y.
3. Plot the x-intercept and y-intercept on the coordinate plane.
4. Draw a straight line passing through these two points to represent the graph of the equation.