Question

How do you find the intercepts for `4x+3y=8`?

Answer 1

`x`-intercept`(2,0)`
`y`-intercept`(0,8/3)`

Explanation:

To find the `x`-intercept, substitute `y=0`,

`4x=8`
`x=2`

To find the `y`-intercept, substitute `x=0`,

`3y=8`
`y=8/3`

Hence, the `x`-intercepts and `y`-intercepts are `(2,0)` and `(0,8/3)` respectively.

Answer 2

The graph intersects the `X` axis in `P_1(2,0)` and the `Y` axis in `P_2(0,8/3)`.

Explanation:

The graph intersects the `Y` axis when `X=0` and the `X` axis when `Y=0`. Therefore, taking `4x+3y=8` and the cases:

1. When `x=0`:
   `3y=8 => y=8/3`
   `P_2(0,8/3)`

2. When `y=0`:
   `4x=8 => x=8/4=2`
   `P_1(2,0)`

graph{4x+3y=8 [-7.024, 7.02, -3.51, 3.51]}