A linear function is represented by f(x)=2x+7. What would be the parallel to the function?

Question

How would you show a parallel graph to the function usin f(x)=2x-7?

Answer 1

Hi, Carmen.

When working with functions, you can replace the f(x) with y. This linear function is in the slope-iintercept form, y = mx + b, and the slope of this line = 2.

Parallel lines have the same slope, so any line with a slope of 2 would be parallel to this one. Any function in the form f(x) = 2x + ? would be parallel.

Hope this helps!

 

Answer 2

Expanding on the previous answer:

     Lets set up the equations    2X+7= Y

                                             2x -7 = y     We know that m = 2  

                                            and m = (y-Y)/(x-X)

   Substitution:                      (2x-7 - 2X+7)/( x-X)  = 2 therefore they are                        

                                           parallel having the same slope.

                                                 

    now:                                (2x+b - 2X +B)/( x-X)  = 2           let X = 0

                                                 

    Then:                               2x + (b-B) = 2x   and   1+(b-B)/2x = 1    

                                            and   (b-B)/2x = 1

let (b-B) = a constant b, then:         b/2 = x, and generalizing let m = 2  then  b = mx which is:

                           mx-b = 0 the general solution

where x and b are R (real numbers) and if m remains constant any linear combinations of mx - b results in a solution of parallel lines