To determine which expression represents "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]", let's break down the phrase step by step:
1. Difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]:
- The difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex] is mathematically expressed as [tex]\( t - y \)[/tex].
2. Three times the difference:
- To find three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex], we need to multiply the difference ([tex]\( t - y \)[/tex]) by 3.
- This gives us [tex]\( 3(t - y) \)[/tex].
Now, let's examine the provided options to see which one matches our expression [tex]\( 3(t - y) \)[/tex]:
1. Option 1: [tex]\( y - 3t \)[/tex]
- This expression represents [tex]\( y \)[/tex] minus three times [tex]\( t \)[/tex], which is not the correct interpretation of "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]".
2. Option 2: [tex]\( 3t - y \)[/tex]
- This expression represents three times [tex]\( t \)[/tex] minus [tex]\( y \)[/tex], which also does not match "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]".
3. Option 3: [tex]\( 3(t - y) \)[/tex]
- This expression correctly represents three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex] because it multiplies the difference [tex]\( t - y \)[/tex] by 3.
Therefore, the correct expression that represents "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]" is
[tex]\[ 3(t - y) \][/tex]
