Sure, let's complete the table for the relation [tex]\( y = 5 + 2x \)[/tex]. We'll fill in the values of [tex]\( y \)[/tex] corresponding to selected values of [tex]\( x \)[/tex].
Here is the completed table:
| [tex]\( x \)[/tex] | [tex]\( y \)[/tex] |
|----------|----------|
| [tex]\(-10\)[/tex] | [tex]\(-15\)[/tex] |
| [tex]\(-9\)[/tex] | [tex]\(-13\)[/tex] |
| [tex]\(-8\)[/tex] | [tex]\(-11\)[/tex] |
| [tex]\(-7\)[/tex] | [tex]\(-9\)[/tex] |
| [tex]\(-6\)[/tex] | [tex]\(-7\)[/tex] |
| [tex]\(-5\)[/tex] | [tex]\(-5\)[/tex] |
| [tex]\(-4\)[/tex] | [tex]\(-3\)[/tex] |
| [tex]\(-3\)[/tex] | [tex]\(-1\)[/tex] |
| [tex]\(-2\)[/tex] | [tex]\(1\)[/tex] |
| [tex]\(-1\)[/tex] | [tex]\(3\)[/tex] |
| [tex]\( 0 \)[/tex] | [tex]\(5\)[/tex] |
| [tex]\( 1 \)[/tex] | [tex]\(7\)[/tex] |
| [tex]\( 2 \)[/tex] | [tex]\(9\)[/tex] |
| [tex]\( 3 \)[/tex] | [tex]\(11\)[/tex] |
| [tex]\( 4 \)[/tex] | [tex]\(13\)[/tex] |
| [tex]\( 5 \)[/tex] | [tex]\(15\)[/tex] |
| [tex]\( 6 \)[/tex] | [tex]\(17\)[/tex] |
| [tex]\( 7 \)[/tex] | [tex]\(19\)[/tex] |
| [tex]\( 8 \)[/tex] | [tex]\(21\)[/tex] |
| [tex]\( 9 \)[/tex] | [tex]\(23\)[/tex] |
| [tex]\(10\)[/tex] | [tex]\(25\)[/tex] |
In this table:
- For [tex]\( x = -10 \)[/tex], the corresponding [tex]\( y \)[/tex] value is [tex]\( -15 \)[/tex].
- For [tex]\( x = -9 \)[/tex], the corresponding [tex]\( y \)[/tex] value is [tex]\( -13 \)[/tex].
- For [tex]\( x = -8 \)[/tex], the corresponding [tex]\( y \)[/tex] value is [tex]\( -11 \)[/tex].
- (... continue for all values of [tex]\( x \)[/tex] in the range ...)
For each given [tex]\( x \)[/tex] value, we calculate the value of [tex]\( y \)[/tex] using the relationship [tex]\( y = 5 + 2x \)[/tex]. This way, we can determine the corresponding [tex]\( y \)[/tex] value for all selected [tex]\( x \)[/tex] values and complete the table accordingly.
