Question

Graph each line y -7 = x + 4

Answer 1

Given the the equation:  y − 7 = x + 4 ;

We should rewrite the equation in "slope-intercept form" ; that is:

           " y = mx + b " ;
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 in which: "y" remains an isolated variable on the "left-hand side" of the equation (with "no coefficients"—except the "implied coefficient of "1"
                 {since "1" , multiplied by any value, results in that same value} ;

                 "m" refers to the "slope" of the line;
                        and "m" is the coefficient of "x" ;

                       "b" refers to the "y-intercept" of the graphed (linear) equation; or more precisely, the value of "y" of the coordinate of the [ point on the graphed line of the equation—where the line crossed the "y-axis" ] ; that is; the  "y-coordinate of the "y-intercept" ; that is, the value of "y" when "x = 0" ; 
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          {Note that:  "m" (the slope) may be a negative value; & that:  "y" may be a negative value; as regard to the "slope-intercept form" equation:
   that is:    
                    "y = mx + b"  . }.
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    So; given the equation:
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 "  y − 7 = x + 4 " ; 
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    Add "7" to each side of the equation; 
to isolate "y" on one side of the equation;
          → {specifically, the "left-hand-side" of the equation} ;

and to rewrite the equation in "slope-intercept form" ; that is;
  →  to rewrite the equation in the format:
                   " y = mx + b " ;
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As such:  "y − 7 = x + 4 " ; 
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→ Add "7" to each side of the equation:
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         → y − 7 + 7 = x + 4 + 7 ;

to get:
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                  →  y = x + 11  ; 
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Now, let us graph the equation:
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Let us make a table:
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   x   ║ (x + 11)       ║    y   ║
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 -20 ║ (-20 + 11)   ║  -9   ║

-19   ║ (-19 + 11)    ║  -8   ║

-18   ║ (-18 + 11)    ║  -7   ║

-17   ║ (-17 + 11)    ║  -6   ║

-16   ║ (-16 + 11)   ║  -5   ║

-15   ║ (-15 + 11)   ║  -4   ║  

-14   ║ (-14 + 11)   ║  -3   ║
 
-13   ║ (-13 + 11)   ║  -2   ║

-12   ║ (-12 + 11)   ║  -1    ║ 

-11    ║ (-11 + 11)    ║   0   ║

-10   ║ (-10+ 11)    ║   1    ║

-9    ║ (-9 + 11)     ║   2   ║

-8    ║ (-8 + 11)     ║   3   ║

-7    ║ (-7 + 11)     ║   4   ║

-6    ║ (-6 + 11)    ║   5   ║

-5    ║ (-5 + 11)    ║   6   ║

-4    ║ (-4 + 11)    ║   7   ║

-3    ║ (-3 + 11)    ║   8   ║

-2    ║ (-2 + 11)    ║   9   ║ 

-1     ║ (-1 + 11)    ║   10  ║

0     ║ (0 + 11)    ║   11   ║

1      ║ (1 + 11)     ║   12  ║

2     ║ (2 + 11)    ║   13  ║

3     ║ (3 + 11)    ║   14  ║

4     ║ (4 + 11)    ║   15  ║

5     ║ (5 + 11)    ║   16  ║
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Now, we plot these points on a graph, and draw a line through these points; the slope is "1" ; since the equation is:  
 " y = x + 11 " ;  Note:  The slope, "m", is "1", since there is an "implied coefficient of "1" ;  i.e. " y = 1x + 11 " .
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Graph of:  "y = x + 11 " ;
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