What is the x and y intercept of x−y=5?

1 Answer
Tanish J.
Nov 30, 2014

Intercepts are the points where the graph crosses the coordinate axes.

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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 =(5,0)

2. To find y intercept

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

0−y=5
y=−5

Therefore, y intercept =(0,−5)

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

xa+yb=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:

x5−y5=1

⇒x5+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=(5,0)
b=−5 and y intercept=(0,−5)

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