Question

Find the $x$ and $y$ intercepts for the line $y = x + 5$.

Answer 1

The $x$ - intercept and the $y$ - intercept, respectively indicates the points where the line cuts the $x$ - axis and the $y$- axis respectively.

Complete step by step solution:
To find the $x$ - intercept and the $y$ - intercept, we need to find the points on the $x$ - axis and the $y$- axis where the line cuts the axes.
To find the $x$ - intercept we need to find the point on the $x$ - axis, hence the ordinate of this point will be $0$. Therefore to obtain the abscissa of this point i.e. equal to the $x$ - intercept, substitute $y = 0$ in the given equation of the line.
Putting $y = 0$, in $y = x + 5$,
$0 = x + 5$
$\Rightarrow x + 5 = 0$
$\Rightarrow x = - 5$
Hence, the $x$ - intercept of the line is $- 5$.

To find the $y$ - intercept we need to find the point on the $y$ - axis, hence the abscissa of this point will be $0$. Therefore to obtain the ordinate of this point i.e. equal to the $y$ - intercept, substitute $x = 0$ in the given equation of the line.
Putting $x = 0$, in $y = x + 5$,
$y = 0 + 5$
$\Rightarrow y = 5$
Hence, the $y$ - intercept of the line is $5$.

Additional information:
The concept of intercept can be visualised from the adjoining graph.

Note:
Since the line given in the question is in the slope intercept form hence, we can also find the $y$ - intercept directly. The line is in the form $y = mx + c$ where $m =$ slope of the line, $c =$ $y$ - intercept. Therefore comparing the equation $y = x + 5$ with the slope-intercept form, the $y$ - intercept is equal to $5$.