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

2 Answers
May 8, 2016

Please see below.

Explanation:

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.

May 8, 2016

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.

Explanation:

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)