Question

Okay, SO, I am taking a math assignment and have a few questions. Thx for the help. MC
PS. only 5 questions, directly from a 25 question assignment...Thanks again!


1.
What is the slope-intercept form of the function that contains the point (6, 2) and has a slope of 3?
y = ___ x + ___


2.
What is the slope-intercept form of the function that contains the point (6, 2) and (4, 8)?
y = ___ x + ___


3.
What is the slope-intercept form of the function described by this table?

x | 1 | 2 | 3 | 4
y | 1 | -2 | -5 | -8


y = ___ x + ___



4.
Bianca makes an initial deposit to open a savings account. She then makes monthly deposits of equal amounts. The balance in her account is given by the function equation B = 150 + 80d, where B is her account balance and d is the number of monthly deposits she makes.

What is the meaning of the slope in this equation?

A. Bianca deposits $80/month.
B. Bianca deposits $150/month.
C. Bianca makes an initial deposit of $80.
D.Bianca makes an initial deposit of $150.

5.
Marcus is eating a meal that is made up of an entree that is 45 calories per ounce and a side dish that is 30 calories per ounce. He wants his meal to total 510 calories. Let e represent the number of ounces of the entree that he eats, and let s represent the number of ounces of the side dish he eats.

Which function relates the number of ounces the side dish that he eats to the number of ounces of the entree that he eats?

A. s = 2/3e - 17
B. s = 3/2e - 11 1/3
C. s = -2/3e + 11 1/3
D. s = -3/2e + 17


Thanks again for the help. will pick as best to anyone who explains how they got their answers.

Answer 1

1.  Line L  slope intercept form :  y = m x + c
     slope m = 3    the point   x = 6, y = 2 lies on L.
     2 = 3 * 6 + c          =>  c = -16
     L =  y = 3 x - 16

2.  L:     y = m x + c
       slope m = (y1 - y2) / (x1 - x2) = (2 - 8) / (6 - 4) = -3
         Since point (6, 2) lies on L,
           2 = -3 * 6 + c      =>  c = 20
       L =  y = -3 x + 20

3.    you can observe that  as x increases by 1, y decreases by 3.  So Slope m is equal to -3.     You can also find it as (-2 - 1) / ( 2 - 1) = - 3

       the point (1, 1) lies on   y = -3 x + c
             1 = -3 + c  => c = 4
   L :  y = -3 x + 4

4.      B balance = $ 150 + $ 80  d,  d is the number of monthly deposits.
       At the beginning, he deposited $150 one time.  and  then each month, the balance increases by $ 80,  Hence he makes a monthly deposit of $ 80.  The slope is $ 80.  Because, each  when  d increases by 1,  B increases by $ 80.

5. 
     entree = 45 cal / ounce
     side dish = 30 cal /ounce
     total energy desired = 510 cal
  number of ounces of entree * calories / ounce
            +  number of ounces of side dish * calories / ounce = total calories.

        e * 45 + s * 30  = 510        , simplifying this we get
           e * 9 + s * 6 = 102
           3 e + 2 s = 34
           s = 17 - 3 e / 2
   it is option D.