solve b^2=-24-11b

Question

1.solve b^2=-24-11b

 

2. write equation in slope intercept form if possible of the line through the pair of points (-10-3)(-10-8)

Answer 1

b²=-24-11b

Turn this into a quadratic equation of 

form ax²+bx+c...  add 11b+24 to both sides

 

b²+11b+24=0

this is factorable.  The factors of 24 that add to 

11 are (3)(8) so this factors to...

(b+3)(b+8)=0

Either b+3=0    or    b+8=0

          b=-3      or    b=-8

 

Check:  b²=-24-11b 

                                     (-8)²=-24-11(-8)

           (-3)²=-24-11b      64=-24+88

            9=-24-11(-3)       64=64

            9=-24+33

            9=9

Both answers check as correct

 

2). (-10,-3), (-10,-8)

      Slope intercept form:  y=mx+b

      slope m= (-8-(-3))/(-10-(-10))

      slope m=-5/0

      The slope is undefined because this is a vertical line.

      You cannot write this line in slope intercept form. 

       The equation of the line is x=-10. 

      y is not a dependent variable and can be any real number.

 

Answer 2

1.  To "solve" means to find the value of b that satisfies the equation.

      b^2 = -24 - 11b

      b^2 + 11b + 24 = 0       (add 11b + 24 to both sides)

      (b+3)(b+8) = 0            (either factor or use quadratic formula)

      b = -3   or   b = -8             (there are two roots)

 

2.  In slope-intercept form ( y = mx + b ), the slope, m, is the change in y divided by the change in x,

                    or "rise" over "run"

         for this problem,

                     (-8 - (-3)) / ((-10) - (-10))           (using the two points)

         This makes the denominator 0 and the quotient undefined, so the slope is undefined.

However, note that in Standard Form, we may express this line very simply as   x=-10.

 

                                                                                                        {WyzAnt e-tutor}