Question

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

Answer 1

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`.

Answer 2

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)`