Question

How do you find the x and y intercepts for `4x - y = 10`?

Answer 1

The x-intercept is the point where the y-value is zero, and vice versa. Substituting 0 in for `x` and `y` in turn and solving gives `x-"intercept"=(10/4,0), y-"intercept" = (0,-10)`.

Explanation:

The x-intercept for a function is the point where it crosses the x-axis, and that is the horizontal line '`y=0`'. Substitute in `y=0` in the original equation to find the x-intercept:

`4x-0=10`
`4x=10`
`x=10/4` `(or 2.5)`

The x-intercept, therefore, is the point `(10/4,0)`.

Similarly, the y-intercept is the point where the function crosses the y-axis, the line `x=0`, so substitute in `x=0`:

`0-y=10`
`y=-10`

So the y-intercept is the point `(0,-10)`.