Question

How do you find the x and y intercepts for `5x+2y=10`?

Answer 1

The `x` intercept is`(2,0)`, and the `y` intercept is `(0,5)`.

Explanation:

We need to find the points in which the line crosses each axis.

The line crosses the `x` axis in a point of the form `(x_0,0)`. If such a point belongs to the line, then it satisfies its equation, so

`5x_0 + 2*0 = 10 -> 5x_0 = 10 -> x_0=2`

The line crosses the `y` axis in a point of the form `(0,y_0)`. If such a point belongs to the line, then it satisfies its equation, so

`5*0 + 2y_0=10 -> 2y_0=10 ->y_0=5`