Question

Darius is 6 years younger than his brother Ty. Represent the relationship between the brother's ages.
Complete the table and write the equation used to represent that relationship.
(5 points)
Darius' age, x
Ty's age, y
0x
6y
6x
12y
10x
16y
12x
18y
Equation:

Answer 1

To represent the relationship between the ages of Darius and Ty, we know that Darius is 6 years younger than Ty. Therefore, if we let \( x \) be Darius' age and \( y \) be Ty's age, we can express this relationship with the equation:

\[ y = x + 6 \]

or equivalently,

\[ x = y - 6 \]

Now we can fill in the table by expressing Ty's age in terms of Darius' age based on the equation \( y = x + 6 \).

### Table:
| Darius' Age (x) | Ty's Age (y) |
|------------------|--------------------|
| 0 | \( 0 + 6 = 6 \) |
| 6 | \( 6 + 6 = 12 \) |
| 10 | \( 10 + 6 = 16 \) |
| 12 | \( 12 + 6 = 18 \) |

### Equation:
The equation that represents the relationship between their ages is:

\[ y = x + 6 \]

where \( y \) is Ty's age and \( x \) is Darius' age.