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.,

#x/a+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:

#x/5-y/5=1#

#=> x/5+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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