Question

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

Answer 1

I found:
`(1,0)`
`(0,1/2)`

Explanation:

x-intercept:
set `y=0`
you get:
`0=-x+1`
so `x=1`

y-intercept:
set `x=0`
you get:
`2y=1`
so `y=1/2`

Answer 2

`( x, y ) -> ( 0, 1/2) " and " (1, 0 )`

Explanation:

The final answers are at parts ( 2 ) and ( 3 )

Before you can determine the intercepts you need to manipulate the equation so that you only have y on the left hand side of the equals sign and everything else on the other side.
To isolate y and still maintain balance multiply both sides by `1/2`

Step1. `" " 1/2( 2y) = 1/2(-x+1)`

`2/2 y = -1/2 x + 1/2`

But `2/2 = 1` giving;

`y= -1/2x + 1/2` .........................( 1 )

Now to find the intercepts:

.*******
Step2. The graph crosses the x-axis at y=0

Substitute y=0 in (1) giving:

`0 = -1/2x + 1/2`

Add `1/2x` to both sides so that you may part isolate `x`

`( 0 ) + 1/2x =(-1/2x+1/2) + 1/2x`

`1/2x=1/2`

Multiply both sides by 2 giving:

`x=1`
so one of the points where it crosses is at `y=0 , x =1` ......( 2 )

.**********
Step3. The graph crosses the y-axis at x=0

Substituting y = 0 in equation ( 1 ) gives:

`y = 1/2` ....................( 3 )
so the other point where it crosses is at `y=1/2, x=0` .......( 3 )