# How do you find the x and y intercepts for 3x+y=6?

May 19, 2016

x- intercept: $\left(2 , 0\right)$
y-intercept: $\left(0 , 6\right)$

#### Explanation:

The x-intercept is the point at which the graph crosses the x-axis. Therefore, the y-coordinate at this point is zero. Knowing this, we can plug in $0$ for $y$ and solve the equation for $x$:

$3 x + y = 6$
$3 x + 0 = 6$
$3 x = 6$
$x = 2$
So, the x-intercept is at $\left(2 , 0\right)$.

Likewise, the y-intercept is the point at which the graph crosses the y-axis, and therefore the x-coordinate will be $0$. So we plug in $0$ for $x$ and solve for $y$:

$3 x + y = 6$
$3 \left(0\right) + y = 6$
$0 + y = 6$
$y = 6$
So, the y-intercept is at $\left(0 , 6\right)$.