# How do you find the x and y intercept of 4x + 4y = 12?

Jul 2, 2016

Intercept on $x$-axis is $3$ and intercept on $y$-axis is also $3$.

#### Explanation:

In $4 x + 4 y = 12$, we can find intercept on $x$-axis by putting $y = 0$ and intercept on $y$-axis by putting $x = 0$.

Hence intercept on $x$-axis is $4 x + 4 \times 0 = 12$ or $4 x = 12$ or $x = 3$.

and intercept on $y$-axis is $4 \times 0 + 4 y = 12$ or $4 y = 12$ or $y = 3$.

Alternatively if intercepts on $x$-axis and $y$-axis are $a$ and $b$ respectively, then equation of line is $\frac{x}{a} + \frac{y}{b} = 1$. Hence, we can also find intercepts on $x$-axis and $y$-axis by converting the equation in this form.

Now $4 x + 4 y = 12 \Leftrightarrow \frac{4 x}{12} + \frac{4 y}{12} = 1$ or

$\frac{x}{3} + \frac{y}{3} = 1$ and hence again we get that intercept on $x$-axis is $3$ and intercept on $y$-axis is also $3$.