Question

How do you find the slope and intercept of `x-2y=0`?

Answer 1

Slope `= 1/2`
y-intercept: `0` (i.e. at `(0,color(green)(0))`
x-intercept: `0` (i.e. at `(color(green)(0),0)`

Explanation:

For a linear equation in the general form:
`color(white)("XXX")color(red)(A)x+color(blue)(B)y=C`
the slope is given by the equation:
`color(white)("XXX")m=-color(red)(A)/color(blue)(B)`

In this case
`color(white)("XXX")x-2y=0color(white)("XXX")rArrcolor(white)("XXX")color(red)(1)x+(color(blue)(-2)y) =0`

and therefore
`color(white)("XXX")m=-(color(red)(1)/(color(blue)(-2)))=1/2`

The y-intercept is the value of `y` when `x=color(cyan)(0)`
`color(white)("XXX")(color(cyan)(0)-2y=0) rarr (y=0)`

The x-intercept is the value of `x` when `y=color(orange)(0)`
`color(white)("XXX")(x-2(color(orange)(0))=0) rarr (x=0)`