# How do you find the x and y intercept given y=3x-6?

##### 1 Answer
Nov 14, 2015

Plug in $0$ for $y$ and $x$, respectively.

#### Explanation:

To find the x-intercept, that is, where the line touches the x-axis, the y-value is equal to $0$. Therefore, in order to find the x-intercept, plug $0$ into $y$ in the original equation.

You get: $0 = 3 x - 6$
Now, you must solve for $x$.
Add $6$ to both sides: $6 = 3 x$
Divide both sides by $3$: $2 = x$
Knowing that $x = 2$, we know that the x-intercept is $\left(2 , 0\right)$.

We use the same logic to find the y-intercept, at which we know that $x = 0$. So, we will plug that into the original equation.

You get: $y = 3 \cdot 0 - 6$
Multiply: $y = 0 - 6$
Subtract: $y = - 6$
Therefore, the y-intercept is $\left(0 , - 6\right)$.

Another way to find the y-intercept is to recognize that $y = 3 x - 6$ is in the general form $y = m x + b$, in which $b$ is equal to the y-intercept, which, in this case, is $- 6$.