Question

What is the x and y intercept of $x-y=5$?

Answer 1

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 that crosses the y-axis of a graph.

Complete step by step solution:
Given line equation is
$\Rightarrow x-y=5$
To find the x intercept put $y=0$ in the above equation.
$\Rightarrow x-0=5$
$\Rightarrow x=5$
Thus, x intercept is 5.
To find the y intercept put $x=0$in the above equation
By substituting $x=0$in the equation we will get,
$\Rightarrow 0-y=5$
$\Rightarrow y=-5$
Thus, y-intercept is -5.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 5 and y-axis at -5.

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 $x-y=5$
Now we need 1 on the right-hand side of the equation, so divide the whole equation by 5. We have
$\Rightarrow \dfrac{x-y}{5}=\dfrac{5}{5}$
Splitting the terms, we have,
$\Rightarrow \dfrac{x}{5}-\dfrac{y}{5}=\dfrac{5}{5}$
$\Rightarrow \dfrac{x}{5}-\dfrac{y}{5}=1$
That is, we have
$\Rightarrow \dfrac{x}{5}+\dfrac{y}{-5}=1$
On comparing with standard intercept form we have x intercept is 5 and y intercept is -5 in both the cases we have the same answer.