True or false explanation

Question

True or False: The equation y = mx + b shows that no line can have a y-intercept that is numerically equal to its slope. Explain.

Answer 1

It is often difficult to prove that a statement is true; it takes only one case to prove that a statement is false.

 

The slope-intercept form of the equation of a line is:  y = mx + b

    where m=slope  and b=y-intercept

 

The statement is: 

   "... no line can have a y-intercept that is numerically equal to its slope"

 

So. the statement says that b can never equal m.  Is that true or false??

    y = (1)x + 1

    y = (0)x + 0       [note: y=0 is the pretty important x-axis]

    y = 5x + 5

    y = -20x - 20

  ...   need I go on (and on)?

Answer 2

Nonsense. m can be any real number; b can be any number (including zero, in which case no constant term would appear).