A line has equation x=my+b for some real nonzero constants m and b. In terms of m and/or b, what is the slope of this line?

Question

I don't understand the question and what it's asking me.

Answer 1

I am not too happy with David W 's Answer.

 

The given equation is x=my+b and assuming that x is the independent variable, y is the dependent variable, which is the usual case, e.g y = f(x), then we should solve for y, getting y = (1/m)x - (b/m).

 

Therefore slope of this function is 1/m, i.e. reciprocal of a certain number, and the y-intercept is the number (-b/m).

 

 

Answer 2

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

    where:

        m is the slope

      and

       the point (0,b) is the y-intercept [the place where the line crosses the y-axis, at x-0]

 

The "slope" is also the "incline" or "grade" or "slant."  It is a measure of "how steep?"

 

The slope is sometimes referred to as "rise over run" because it is:

              (the increase in the y-values)/(the increase in the x-values)

 

A positive slope means that the line is increasing as you move right; a negative slope means that the line is decreasing as you move right.

 

A slope=1 is a 45º angle and is a steep hill to climb.  A slope=-1 is 45º angle going down and is pretty exciting for a roller coaster or a ski slope (ha! I used the word 'slope').

 

Delete (based on Kenneth S's answer):  In terms of m and/or b, the slope is m.

 

Insert:  Since the problem states that the line has the equation:

            x = my + b

       the slope is the x-coefficient of the equation:

            y = (x-b)/m

            y = (1/m)x - (1/m)b

   The slope of the given line is:   (1/m)