Question

How do you find the x and y intercept given `f(x) = 2/3x + 4`?

Answer 1

x-intercept: `=-6`

y-intercept: `=4`

Explanation:

The given equation of straight line is

`f(x)=2/3x+4`

`y=2/3x+4`

`-2/3x+y=4`

`1/4(-2/3x+y)=1`

`-1/6x+y/4=1`

`x/{-6}+y/4=1`

Above equation is in standard intercept form: `x/a+y/b=1`

which has

x-intercept: `a=-6`

y-intercept: `b=4`

Answer 2

The intercepts are `(-6,0)` on the `x`-axis
and `(0,4)` on the `y`-axis.

Explanation:

`f(x) = 2/3x+4` can be written as `y = 2/3x+4`

This is in slope-intercept form, `y = mx +c` so we immediately know that the `y` -intercept is `4`, the point `(0,4)`
On the `y` -axis the `x` -value is always `0`.

To find the `x`- intercept, set `y=0` because on the `x`-axis the `y`-value is always `0`

`0=2/3x +4" "larr xx 3`

`0 = 2x+12`

`-12 = 2x`

`-6=x" "larr` this is the `x`-intercept

The two intercepts are `(-6,0) and (0,4)`

We could also have changed the original equation to :

`3y = 2x +12" "` which is re-arranged to:

`2x-3y = -12" "larr` this is standard form.

Set `x =0` to get `y = 4" "larr` the `y`-intercept

Set `y=0` to get `x =-6" "larr` the `x`-intercept