1. what is an equation for the line with slope 2/3 and y-intercept 9?
2. what is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1).
3. for the equation -4y = 8x, what is the constant of variation?
4. suppose y varies directly with x, and y = 24 when x=8. what is the value of y when x = 10?

Question 1:

 The generic equation of the line is given by:
 
 Where,
 m: slope of the line
 b: cutting point with the y axis
 Substituting values we have:
 
 
 an equation for the line with slope 2/3 and y-intercept is:
 

 Question 2:

 The standard equation of the line is given by:
 
 Where,
 m: slope of the line
 (xo, yo): ordered pair that belongs to the line
 The slope of the line is:
 
 Substituting values:
 
 
 
 
 We choose an ordered pair:
 
 Substituting values:
 
 Rewriting:
 
 
 An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
 

 Question 3:

 For this case, since the variation is direct, then we have an equation of the form:
  Where,
 k: constant of variation.
 We then have the following equation:
  Rewriting we have:
 
  Therefore, the constate of variation is given by:
 
 
 the constant of variation is:
 

 Question 4:

 For this case, since the variation is direct, then we have an equation of the form:
  Where,
 k: constant of variation.
 We must find the constant k, for this we use the following data:
 y = 24 when x = 8
 Substituting values:
  Clearing k we have:
 
 
 Therefore, the equation is:
  Thus, substituting x = 10 we have that the value of y is given by:
  
 the value of y when x = 10 is:
 

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