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**Hint:**First we find the axis intercept values in the given equation. Also, when it is either $x$ or $y$ values are $0$. Then we have to plot the intercepts for the given equation in the graph. Finally we get the required solution.

**Complete step-by-step solution:**

It is given that the question we have to find the $x - $ intercept and $y - $ intercept for the straight line: $ - x - 7y = 14$

Before we start solving this question, let us see what the $x - $ intercept and the $y - $ intercept which is also known as horizontal intercept and vertical intercept by putting $x = 0{\text{, y = 0 }}$ for each one respectively.

Our equation is linear function; the two intercepts can be calculated as follows:

Substituting $x = 0$ in the given equation ie., $ - x - 7y = 14$

$ \Rightarrow - (0) - 7y = 14$

On rewriting we get,

$ \Rightarrow - 7y = 14$

On dividing \[ - 7\] on both sides we get,

$ \Rightarrow y = \dfrac{{14}}{{ - 7}}$

Let us divide the term and we get,

$ \Rightarrow y = - 2$

Hence we get the $x - $ intercept value.

$\therefore $$x - $ Intercept is $y = - 2$

Also, we need to find $y - $ intercept.

Now we are substitute, $y = 0$ in the given equation,

$ \Rightarrow - x - 7y = 14$

On putting the value of zero in place of $y.$

$ \Rightarrow - x - 7(0) = 14$

Multiplying $7$ by $0$ we get

$ \Rightarrow - x - 0 = 14$

By using the elementary operation, we get

$ \Rightarrow - x = 14$

Dividing the whole number $14$ by $( - 1)$, we get

$ \Rightarrow x = - 14$

$\therefore y - $Intercept is $x = - 14$.

Hence, we get $\therefore $$x - $ Intercept is $y = - 2$

$\therefore y - $ Intercept is $x = - 14$.

**Note:**$x - $ intercept is a point at which the graph intersects $x - axis$. That means we always have $y$ equal to zero Similarly we can say that for the $y - $intercept is a point at which the graph intersects $y - axis.$ That means we always have $x$ equal to zero in the coordinate system.

We have to know about the concept of $x - $ intercept and $y - $ intercept for a straight line, satisfying the condition of $x = 0{\text{ and y = 0}}$ in the equation of the given line.

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