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Find the slope and the equation for the line passing through the point (−6,8) with y-intercept at y=−1y=−1.



1.) Find the slope and the equation for the line passing through the point (−6,8) with y-intercept at y=−1y=−1. 
 a) m= 
b)  The equation for the line in slope-intercept form: 

2.)  The graphs given above show data representing the percentage of women and the percentage of men on weight-loss diets for three selected years after 1987. The lines were drawn to pass through or be near the three points. Estimate the slope and the equation for the line for the percentage of men on diets. 
 a) Slope of the line for the men: m= 
 b) The equation of the line for the men in slope-intercept form: 



3.) Find the slope, mm, and y-intercept of the line y=3x+1. 
 a) m =  
 b) The y-intercept is  

4.) The equation of the line that goes through the points (−2,7)and (3,−3)can be written in the form y=mx+b
m=
 b= 

5.) (a) Put the linear expression 4−9(x+3)+3(4x+4)in the form mx+b
 b) Give the constant term and the coefficient of x in the linear expression 
 4−9(x+3)+3(4x+4)
 The constant term is  
 The coefficient of x is 

6.) A line’s equation is given in point-slope form: 
 y−29=5(x−5)
 This line’s slope is  
 A point on this line that is apparent from the given equation is 

7.) Write an equation for the line through the point (2,9) with slope 5 in point-slope form y=y0+m(x−x0).

8.)  Write an equation for the line through the points (8,10) and (5,4) in point-slope form y=y0+m(x−x0). 

9.)  Find the slope, x-intercept, and y-intercept for the line 2x−10y−16=0

 The slope is 

 The x-intercept is 

 The y-intercept is 

Note: Your answers must be decimals.

10.)  The equation, in general form, of the line that passes through the point (0,5) and is perpendicular to the line 6x+7y+9=0  is Ax+By+C=0, where 
A=
B=
C=

12) *  Fine the equation for the line passing through the point (−4,−1) and parallel to the line whose equation is y=2x+7.

13) Find the value of k so that the line containing the points (3,k) and (−8,1) is perpendicular to the line y=−6/5x−4.

 k=


16.) Find the slope of the line passing through the points (a,−1a+5)(a,−1a+5) and (a+h,−1(a+2h)+5). 
The slope is  

18.)  The equation of the line that goes through the points (−5,−3) and (4,3)( can be written in the form y=mx+b where its slope m is:  


20.)  (a) What is the average rate of change of g(x)=−8−7x between the points (−3,13) and (3,−29)? 

 answer = 
The function g is (increasing or decreasing) on the interval -3 ≤x≤3

21.) Let g(x)=7−8x+4x ² then the expression
g(x+h)−g(x)/h

can be written in the form Ah+Bx+C where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.)
(A) Find the constants. 
A=
B=
C=

22.)  Let f(x)=5x ²+ 3x+3 and let g(h)= f(3+h)-f(3)/h

a) g (1)
b) g (0.1)
c) g (0.01)

 You will notice that the values that you entered are getting closer and closer to a number L. This number is called the limit of g(h)as h approaches 0 and is also called the derivative of f(x) at the point when x=3 We will see more of this when we get to the calculus textbook. 
 Enter the value of L:

23.)  Let f(x)=7−7x+5x². Calculate the following values: 

f(a)=
f(a+h)=
f(a+h)-f(a)/h =

24.)  The height s of a ball (in feet) at time t(in seconds) is given by the formula s(t)=64−16(t−1)². Consider the following expression. 

 Compute the value of AV[0.5,1]

26.) An open box is to be made from a flat piece of material 16 inches long and 5 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors. 
 V(x)= 

If we write the domain of V(x) as an open interval in the form (a,b)(a,b), then what is a? 

a=
 and what is b?
b=


30.) The domain of the function
g(x)=√x(x-17)

is=
Note: Write the answer in interval notation. If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter −∞as - infinity and ∞ as infinity . 

31.)  The domain of the function
f(x)=√2x-62




32.)  Express the function f(x)=3|x−2|−|x+4| in piece wise form without using absolute values. [Suggestion: It may help to generate the graph of the function.]

f(x)={ f1 x ≤ a 
        { f2  a<x<b 
        { f3   x≥b

a=
b=
f1=
f2=
f3=

  
33.) Find f(0),f(7),f(−7),f(3) and f(7–√) for


 f(x)={2/x   if x>3
          {3x    if x≤3

f(0)=
f(7)=
f(-7)=
f(3)=
f( √-7)=

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