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

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#

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:

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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 )

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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 )