Question

What are the intercepts of the line `y = 1/2x-3`?

Answer 1

x-intercept `= 6`
y-intercept `=-3`

Explanation:

The x-intercept is the point where the graph crosses the X-axis; for all point on the X-axis, `y=0`
Substituting `0` for `y` in `y =1/2x-3`
we get
`color(white)("XXX")0=1/2x-3`

`rarrcolor(white)("XXX")1/2x = 3`

`rarrcolor(white)("XXX")x=6`

Similarly, the y-intercept is the point where the graph crosses the Y-axis; and for all point on the Y-axi, `x=0`
Substituting `0` for `x` in `y=1/2x-3`
we get
`color(white)("XXX")y =1/2*(0) -3`

`rarrcolor(white)("XXX")y=-3`

Answer 2

You set `x` and `y` to `=0` in turn

Explanation:

`y`-intercept is when `x=0`
Then `y=-3->(0,-3)`

`x`-intercept is when `y=0`
`1/2 x-3=0->1/2 x=3->x=6->(6,0)`
graph{0.5x-3 [-6.92, 13.08, -5.76, 4.24]}