Question

How do you find the x and y intercept of \[x - y - 2 = 0\]?

Answer 1

Hint: 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 solution:
Given, \[x - y - 2 = 0\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[\Rightarrow x - 0 - 2 = 0\]
\[\Rightarrow x - 2 = 0\]
Add 2 on both sides of the equation,
\[\Rightarrow x - 2 + 2 = 2\]
\[ \Rightarrow x = 2\].
Thus ‘x’ intercept is 2.
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[\Rightarrow 0 - y - 2 = 0\]
\[ \Rightarrow - y - 2 = 0\]
Add 2 on both sides of the equation,
\[\Rightarrow - y - 2 + 2 = 2\]
\[ \Rightarrow - y = 2\]
\[ \Rightarrow y = - 2\].
Thus ‘y’ intercept is \[ - 2\].
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 2 and y-axis at \[ - 2\].

Note: We can solve this using the standard intercept form. That is the equation of line which cuts off intercepts ‘a’ and ‘b’ respectively from ‘x’ and ‘y’ axis is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]. We convert the given equation into this form and compare it will have a desired result.
Given \[x - y - 2 = 0\]
\[\Rightarrow x - y = 2\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 2. We have,
\[\Rightarrow \dfrac{{x - y}}{2} = \dfrac{2}{2}\]
Splitting the terms we have,
\[\Rightarrow \dfrac{x}{2} - \dfrac{y}{2} = \dfrac{2}{2}\]
\[\Rightarrow \dfrac{x}{2} - \dfrac{y}{2} = 1\]
That is we have,
\[ \Rightarrow \dfrac{x}{2} + \dfrac{y}{{ - 2}} = 1\]. On comparing with standard intercept form we have ‘x’ intercept is 2 and y intercept is \[ - 2\]. In both the cases we have the same answer.