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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
                    |
 \| ]

30.           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!

 \---

)### changes Related to Questions \(:
 m1 =.  What4 is \ the)?
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3. Plot the line on a y coordinate \)- planevalues using the if table \( values x.
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 the5 \(. y How \ do)- weinter writecept of the general the form line of \( a y linear = equation ?

6###x Tip +:  
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 \(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 \( m \).

For the line y = 6x + 3, create a table to show the values of x and y where x is between -1 and 3.

Learn how to create a table of values for the linear equation y = 6x + 3, where x ranges from -1 to 3. Step-by-step calculations and solutions provided for each value of x, showing corresponding y-values. Perfect for Grades 6-8 students studying linear equations and slope-intercept form.

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