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

Nov 30, 2014

Intercepts are the points where the graph crosses the coordinate axes. Notice how at the Y Intercept the value of the x-coordinate is 0, and at the X Intercept, the value of the y-coordinate is 0. We can use this principle to find the x and y intercepts!

1. To find x intercept

Substitute $y = 0$ in the given equation, and solve for $x$.

$x - 0 = 5$
$x = 5$

Therefore, x intercept $= \left(5 , 0\right)$

2. To find y intercept

Substitute $x = 0$ in the given equation, and solve for $y$.

$0 - y = 5$
$y = - 5$

Therefore, y intercept $= \left(0 , - 5\right)$

Another way to do this in to remember the intercept form of an equation of a line, i.e.,

$\frac{x}{a} + \frac{y}{b} = 1$

where
$a$ is the x-intercept
$b$ is the y-intercept

Given equation: $x - y = 5$
To make the RHS = 1, we'll divide throughout by 5, getting:

$\frac{x}{5} - \frac{y}{5} = 1$

$\implies \frac{x}{5} + \frac{y}{-} 5 = 1$

Notice how this looks like the intercept form of an equation of a line.

Comparing the two equations, we can conclude
$a = 5$ and x intercept$= \left(5 , 0\right)$
$b = - 5$ and y intercept$= \left(0 , - 5\right)$