How do you find the intercepts for \[x + 5y = 0\] ?

Hint: Here we need to find ‘x’ and ‘y’ intercepts. X-intercept can be found by substituting the value of ‘y’ is equal to zero in the given equation. Similarly we can find the y-intercept by substituting the value of ‘x’ equal to zero in the given equation. In other words ‘x’ intercept is defined as a line or a curve that crosses the x-axis of a graph and ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph.

Complete step by step answer:
Given, \[x + 5y = 0\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[x + 5(0) = 0\]
\[ \Rightarrow x = 0\].
Thus ‘x’ intercept is 0.
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[0 + 5y = 0\]
\[ \Rightarrow y = 0\].
Thus ‘y’ intercept is 0. If we draw the graph for the above equation. The line or curve passes through the origin.

Hence, the ‘x’ intercept is 0 and ‘y’ intercept is also 0.

Note:We can write the given equation in the form of slope intercept form that is \[y = mx + c\]. Where ‘m’ is slope and ‘c’ is y intercept.
\[x + 5y = 0\]
Rearranging we have,
\[5y = - x\]
Divide by 5 on both sides of the equation,
\[y = - \dfrac{1}{5}x + 0\].
When comparing with the standard slope intercept equation we have,
Slope is equal to \[ - \dfrac{1}{5}\] and y-intercept is 0. If we want an x-intercept we put ‘y’ is equal to zero in the given equation. We will have an answer which is the same as above.