Question

How do you find the x and y intercepts for `3x+2y=1`?

Answer 1

x-intecept = `1/3` , y-intercept = `1/2`

Explanation:

If you write the equation as follows :

`2y = -3x + 1`

`rArr` `y = (-3x)/2 + 1/2`

And compare it to the slope intercept form of linear equations,
You find that y-intercept is `1/2`.

And If you do this :

`3x = -2y + 1`

`rArr` `x = (-2y)/3 + 1/3`

Here, the x - intercept is `1/3`.

See in the graph:

graph{3x + 2y = 1 [-1.199, 1.202, -0.599, 0.601]}

Answer 2

Intercept on `x`-axis is `1/3` and on `y`-axis is `1/2`

Explanation:

There are two ways of doing this.

One - If a line has intercepts `a` on `x`-axis and `b` on `y`-axis, then its equation is `x/a+y/b=1`

Now we can write `3x+2y=1`

as `x/(1/3)+y/(1/2)=1`

Hence, intercept on `x`-axis is `1/3` and on `y`-axis is `1/2`

Two - We can find `x` intercept by putting `y=0` and `y` intercept by putting `x=0` (this method is applicable even on non-linear equations.

Putting `y=0` we get `3x=1` or `x=1/3` and putting `x=0`, we get `2y=1` or `y=1/2`.

Hence, intercept on `x`-axis is `1/3` and on `y`-axis is `1/2`

graph{3x+2y=1 [-2.532, 2.47, -0.96, 1.54]}