Help with math homework.?

Question

1) write the equation in the slope-intercept form for the line that passes through A(3,-4) and B (11,8)

2)Expand and simplify: (2x^2 - 6y)(3x^2 + 7y)

3) Factor 6m^2 + 23m -18

Answer 1

1) Given that,

     The points through which the line passes are A = (3,-4) and B = (11,8)

     The equation of the line passing through the points A(3,-4) and B (11,8) in slope intercept form is

                      y = mx + c   -> (1)

                                    where m = slope of the line and b = y-intercept

     To find the slope m, of the line is the change in y divided by change in x

                             x1 = 3, y1 = -4

                             x2 = 11, y2 = 8

                        i.e, m = (y2 - y1)/(x2-x1)                   

                                   = (8+4)/(11-3)

                                   = 12/8

                                   = 3/2.

  To find the y-intercept b, substitute one of the points in the eauation (1)

   Let us take point A(3,-4)

                 y = mx + b

          => -4 = (3/2)(3) + b

          => -4 = 9/2 + b

          => -4-9/2 = b

          => b = (-8-9)/2

          => b = -17/2

  Now we know the values of slope, m=3/2 and y-intercept, b=-17/2.

  Hence we can write the equation of the line y = 3x/2 -17/2.

Answer 2

2) Given expression is  (2x^2 - 6y)(3x^2 + 7y)

                                  = ( (2x^2)(3x^2) + (2x^2)(7y) - (6y)(3x^2) -(6y)(7y) )    [ (a-b)(c+d) = ac+ad-bc-bd ]

                                  = ( 6x^4 + 14x^2y - 18x^2y - 42y^2 )                          [ a*a = a^1+1=a^2 ]

                                  = 6x^4 -4x^2y -42y^2

                                 

Answer 3

3) Given expression is 6m^2 + 23m -18

     To find the factor we have the formula 

and

Therefore the possible solutions are m=

and

Comments

Factor of 6m² + 23m - 18 = (2m + 9)(3m - 2).

Answer 4

(3).

The trinomial expression is 6m² + 23m - 18.

Multiply first term 6m² and last term - 18 = - 108m²

The correct pair of the terms 27m and - 4m multiply to - 108m² and add to 23m.

Replace the middle term 23m with 27m - 4m.

= 6m² + 27m - 4m - 18

Group the terms into two pairs.

= (6m² + 27m) + ( - 4m - 18)

Factor out 3m from the first group  and factor out - 2 from the second group.

= 3m(2m + 9) - 2(2m + 9)

Factor out common term 2m + 9.

= (2m + 9)(3m - 2)

Factor of 6m² + 23m - 18 = (2m + 9)(3m - 2).