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

x-intecept = $\frac{1}{3}$ , y-intercept = $\frac{1}{2}$

#### Explanation:

If you write the equation as follows :

$2 y = - 3 x + 1$

$\Rightarrow$ $y = \frac{- 3 x}{2} + \frac{1}{2}$

And compare it to the slope intercept form of linear equations,
You find that y-intercept is $\frac{1}{2}$.

And If you do this :

$3 x = - 2 y + 1$

$\Rightarrow$ $x = \frac{- 2 y}{3} + \frac{1}{3}$

Here, the x - intercept is $\frac{1}{3}$.

See in the graph:

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

May 9, 2017

Intercept on $x$-axis is $\frac{1}{3}$ and on $y$-axis is $\frac{1}{2}$

#### 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 $\frac{x}{a} + \frac{y}{b} = 1$

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

as $\frac{x}{\frac{1}{3}} + \frac{y}{\frac{1}{2}} = 1$

Hence, intercept on $x$-axis is $\frac{1}{3}$ and on $y$-axis is $\frac{1}{2}$

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 $3 x = 1$ or $x = \frac{1}{3}$ and putting $x = 0$, we get $2 y = 1$ or $y = \frac{1}{2}$.

Hence, intercept on $x$-axis is $\frac{1}{3}$ and on $y$-axis is $\frac{1}{2}$

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