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					No Graphs are needed only the problems


Q1. Graph the line with the given point and slop. (Do them one by one.)

a. The line through (2, 5) with slop-1
      y-5=-(x-2)
i.e.,
       y=-x+7




b. draw a line 1/1 through (0,3) with slop 1 and line ½ through (0,0) with slop 1.
Line through (0,3) with slop 1 : y=x+3
Line through (0,0) with slop 1 : y=x
C Draw 1/i( underneath small 1) (0. -3) and (3, 0) what is the slop of any line
perpendicular t 1/i? draw ½ through the origin so that it is perpendicular1/i
      The slope of the line (0. -3) and (3, 0) is
                        k  0 (03)  1
                              3
So, the slop of any line perpendicular t 1/i is -1/1 =-1
So, the line through the origin so that it is perpendicular1/i is
              y=-x




d. Find the slop and y- intercept for each line that has a slop and y- intercept
   x- y = 4

Since x-y=4, we have
                y=x-4
So, the slope is 1 and Y- intercept is -4.
e. Draw a graph of each line using its y intercept and its slop y=3/2x -4
Q2. The annual social security benefit of a retiree depends on the age at the time of
retirement. the accompanying graph gives the annual benefit for persons retiring at ages
62 through 70 in the year 2005 or later ( source social security administration) what is
the annual benefit for a person who retires at age 64? At what retirement ages does a
person receive an annual benefit of $11600? Find the slop of each line segment on the
graph, and interpret your result. Why do people who postpone retirement until 70 years of
age get the highest benefit?

!!You should provide the graph, otherwise, we can not do anything.

Q3. Find the slope and Y- intercept for each line that has a slope and Y- intercept?

       Y= 2x
Solution. Since Y=2x, the slope is 2 and Y- intercept is 0.


 Q4. Marginal revenue: a defense attorney charge her client $4000 plus $120 per hour.
The formula R= 120n+4000 gives her revenue in dollars for n hours of work. What is her
revenue for 100 hours of work? What is her revenue for 101 hours of work increase the
revenue ( the increase in revenue is called the marginal revenue for the 101 st hour)

 Her revenue for 100 hours of work is given by
                R1= 120n1+4000=120*100+4000=16000
and revenue for 101 hours of work is given by
               R2= 120n2+4000=120*101+4000=16120
So, the increase is R2-R1=120

Q5. Find the equation of each line write each answer in slop intercept form.

The line with slop- 8 that goes through (-1, -5)
y-(-5)=-8[x-(-1)]
so,
         y+5=-8x-8
i.e., y=-8x-13


Q6 The line through (1, 4) with slop ¼

y-4=1/4[x-1]
so,
         y-4=x/4-1/4
i.e., y=x/4+15/4



Q7. Find the equation of each line write each answer standard form using only integers.

The line through the point (-1,-3 and (2,-1)

                   1( 3)
The slope is k    2( 1)     2 , so the equation is
                                3

                   y  (1)  2 ( x  2)
                              3
So,
                y  1  2 ( x  2)  3 y  3  2 x  4  2 x  3 y  7
                        3




Q8. A developer prices condominiums in Florida at $20,000 plus $40 per square foot of
living area. Express the cost C as a function of the number of square feet of living area S.

By hypothesis, it is
     C  20000 40S

Q9 with a GM master card 5% of the amount charges is credited toward a rebate on the
purchase of a new car. Express the rebate R as a function of the amount charged A.

By hypothesis, it is
     R  0.05A


Q10 Graph each inequality (each do them one by one)
A. Y<2x+2




B Y< -2x+1




C   y< ½ x+1
D   y<7




E 3y-5x  15
F –x>70 –y
   y>70+x




Q11. Cost and topping. The cost C in dollars for a pizza with n topping is given by
   C( n) =0.75n +6.99
A find c(2), c(4),and c(5).
C( 2) =0.75*2 +6.99=9.49

C( 4) =0.75*4 +6.99=9.99
C( 5) =0.75*5 +6.99=10.74



B is the cost increasing or decreasing as the number of topping increases?
 Increasing, since the slope is 0.75>0

				
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