Question

Find $x$ and $y$ intercepts of the line $y - x = - 5$.

Answer 1

Hint: $x$ intercept of a line can be obtained by substituting $y = 0$ in the equation of line. Similarly $y$ intercept can be obtained by putting $x = 0$. Put these values in the equation of line one by one to get the $x$ intercept and $y$ intercept respectively.

Complete step-by-step answer:
According to the question, the given equation of line is $y - x = - 5$. The value of $x$ intercept and $y$ intercept of the line is to be determined.
For finding the value of $x$ intercept, we’ll put the value of $y$ to be zero i.e. $y = 0$ in the equation of line. Doing so, we’ll get:
$
   \Rightarrow 0 - x = - 5 \\
   \Rightarrow x = 5
 $
Thus the value of $x$ intercept is 5.
Similarly, for finding the value of $y$ intercept, we’ll put the value of $x$ to be zero i.e. $x = 0$ in the equation of line. Doing so, we’ll get:
$
   \Rightarrow y - 0 = - 5 \\
   \Rightarrow y = - 5
 $
Thus the value of $x$ intercept is -5.
This can be represented in a graph. Follow the below diagram:

Geometrically speaking, the x-intercept of a line is where the line crosses the x-axis and y-intercept is where it crosses y-axis.

Thus the final answer is: $x - {\text{intercept}} = 5$ and $y - {\text{intercept}} = - 5$.

Note: If x and y intercepts of a line are known to us, we can easily determine the equation of line. Let $a$ and $b$ are the x and y intercepts respectively of the line, then the equation of line is:
$ \Rightarrow \dfrac{x}{a} + \dfrac{y}{b} = 1$
And if only y intercept is known along with the slope of line then also its equation can be easily determined. If $m$ is the slope and $c$ is the y intercept of the line, then the equation of line is:
$ \Rightarrow y = mx + c$