7. write the equation of a line that includes the point (1, 5) and has a slope of 3 in slope-intercept form.
a) 3x + y = 2
b) -3x + y = 5
c) -3x + y = 2
d) 3x + y = 5

The answer is:  [C]:  " y = 3x + 2 " .

Explanation:

   In "slope-intercept form" ; the equation is written in the following form:

    " y = mx + b "  ;  with the "y" as a single variable on the "left-hand side" of the equation;  and "m" is slope of the line and coefficient of "x" ;  and "b" is the "y-intercept" (or more precisely, the coordinate of "x" when "y = 0").

   Answer choice:  [C]:  " -3x + y = 2 " ;  written in slope-intercept is as follows.

      Given:  -3x + y = 2 ;  add "3x" to EACH side of the equation ; to isolate "y" as a single variable on the "left-hand side of the equation ;

                 -3x + y + 3x = 2 + 3x  ;

  to get:    y = 2 + 3x  ;  rewrite as: 
                   ↔ " y = 3x + 2 " ; 

             and the equation is in "slope-intercept form" ;  that is:

                   " y = mx + b " ;

in which the slope, "m", equals "3" ;  and the point:  "(1, 5)" is included.

              {that is ; when "x = 1, y = 5 "} ;
 
           →  y = 3x + 2  ;   3(1) + 2 =  3 + 2  = 5 .