We areTo solve this problem and create a table of $x$ given and the y line \ equation) \( values y for = 6x + 3 and asked to create the a line table showing the values y of \( = x and $y$, where x6x \ +) 3 is \ between), \ where(-1 \(\ x) and is between $-1$ (3 and\ ().

Let’s3 substitute values of x \), ( wefrom can \ follow(- these1) to steps (:

13. Substitute specific \ x)) \ into)- thevalues equation in to the find equation \( y the = corresponding \( y-values.

The equation is:
[ y = 6x + 36 x\ +]

###3 Step -by). -step2 Calcul.ations Calculate: the1 corresponding. ( For y ( \ x)- =values -. 13 .): Create
a table \ with[ the results y.

=---

###6 Calcul(-ations1

| $x$ | Substitute into $y = 6x + 3$ | $y$ (Result)) | | +------------- 3 = -6 + 3 = -3 |------------------------------------]

2. For| (---------------- x----- =| |0 - \1):
   | ( \ y[ = y6 =(- 16)( +0 )3 + = -36 = + 03 + \ )3 = | -33 | | ]

3.       For | \( x = \(  y1 = \ ):6  
   

( 0 )[

• y3 = = 60( +1 )3 ) + 3 = |6 + 3 = 39
  | | \ ]

1 | y = 6(1) + 43. = For \(6 x + = 32 \):
| \9[ | y = 6(2) + 3 = 12 + 3| = 152 | \ (]

5. For $x = 3$:
   \ y = [ 6(2) + 3 = 12 + 3 ) | 15 | | 3 | ( y = 6 y( =3 )6 +( 33) = + 183 + = 318 \ +) 3 | = 2121
   |

###]

Final---

Table###

Final| Table ( of x Values : )| | \( x y \) | || (--------- y| ---------)| | -1 | -3 | | 0 | 3 | | 1 | 9 | | || ----------2| ---------- || | $-1$15 | ( - | 3 |) | | ( 30 \ |) | ( 321 \ ) |

| ###| Conclusion ( This1 table \ represents) the values | of \(9 x \) and | | \( 2 y | \ $15)$ | | ( 3 \ for) | the ( line (21 y \ =) |

6x + 3 \Would) you like me within to explain further or help the graph given range this relationship of? ( x

### Related Questions:

1. How would the graph of) ( from y \ =(- 16\x) + to (3 \3) \ look).

likeDo? you2 need. further What clarification happens or if a the graph slope to in visualize ( this y line =? mx Let + me know3!

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)### changes Related to Questions (: m1 =. What4 is \ the)? slope3 of. the How line do ( you y interpret = the slope6 andx y +-inter cept3 of \ ()? y2 =. How6 wouldx the + table change3 if \ the)? equation4 was. What y are = the steps6 tox find - \( 3? 3. Plot the line on a y coordinate )- planevalues using the if table ( values x. )4 includes. What decimals is? the5 (. y How \ do)- weinter writecept of the general the form line of ( a y linear = equation ?

6###x Tip +:
3 \The slope)? (5 m. = What happens6 to \ the) line in this equation tells when you the that for coefficient every of ( increase x of \ ) changes?

1### in Tip (: The x ), equation \( y y \ =) mx increases + by b \6) units represents a line., where \( m is the slope and $b$ is the $y$-intercept. For every change of $x$ by 1, $y$ changes by $m$.