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**Hint:**Here we need to find x-intercept and y-intercept. We know that x-intercept is a point on the graph where ‘y’ is zero.

Also we know that y-intercept is a point on the graph where ‘x’ is zero. In other words the value of ‘x’ at ‘y’ is equal to zero is called x-intercept. The value of ‘y’ at ‘x’ is equal to zero is called t-intercept. Using this definition we can solve the given problem.

**Complete step by step solution:**

Given,

\[2x + y = 6\].

To find the x-intercept we substitute \[y = 0\] in the given equation we have,

\[2x + (0) = 6\]

\[2x = 6\]

Dividing by 2 on both side of the equation we have

\[x = \dfrac{6}{2}\]

\[x = 3\]

That is x-intercept is 3.

To find the y-intercept we substitute \[x = 0\] in the given equation we have,

\[2(0) + y = 6\]

\[y = 6\]

That is y-intercept is 6.

**Thus, we have the x-intercept is 3. The y-intercept is 6.**

**Note:**We can also solve this by converting the given equation into the equation of straight line intercept form. That is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]. Where ‘a’ is a x-intercept and ‘b’ is called y-intercept.

Now given,

\[2x + y = 6\]

We need 1 on the right hand side of the equation. So we divide the equation by 6 on both sides.

\[\dfrac{{2x + y}}{6} = \dfrac{6}{6}\]

Separating the terms in the left hand side of the equation. We have,

\[\dfrac{{2x}}{6} + \dfrac{y}{6} = \dfrac{6}{6}\]

Now cancelling we have,

\[\dfrac{x}{3} + \dfrac{y}{6} = 1\].

Now comparing with the standard intercept equation we have,

The x-intercept is 4. The y-intercept is 3. In both the methods we have the same answer. We can choose any one method to solve this.

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