Question

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

Answer 1

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 `=(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)`

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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)`