See attached file for full problem description.
1. Find the missing coordinates in the following table:
3. Demand Equation. Helen's Health Foods usually sells 400 cans of Pro Pac Muscle Punch per week when the price is $5 per can. After experimenting with prices for some time, Helen has determined that the weekly demand can be found by using the equation: d = 600 - 40p
Where d is the number of cans and p is the price per can.
a.) Will Helen sell more or less Muscle Punch if she raises her price from $5?
b.) What happens to her sales every time she raises her price by $1?
c.) Graph the equation
d.) What is the maximum price that she can charge and still sell at least on can?
4. Find the slope of each line
5. Graph the line with the given point and slope: the line through ( -2, 5) with slope -1
6. Solve the problem: Draw l1 through (-4,0) and (0,6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1.
7. Retirement pay. 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 (Social Security Administration, www.ssa.gov )What is the annual benefit for a person receive an annual benefit of $11,600? Find the slope of each line segment on the graph, and interpret you results. Why do people who postpone retirement until 70 years of age get the highest benefit?
8. Write an equation for each line. Use slope-interception form if possible.
9. Find the slope and y intercept for each line that has a slope and y intercept. x + 2y = 3
10. Determine whether the lines are parallel, perpendicular, or neither. y = 1/3x + ½; y = 1/3x - 2
11. Marginal Revenue. A defense attorney charges 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? By how much did the one extra hour of work increase the revenue? (The increase in revenue is called the marginal revenue for the 101st hour)
12. Pens and Pencils. A bookstore manager plans to spend $60 on pens at 30 cents each and pencils at 10 cents each. The equation 0.10x + 0.30y = 60 can be used to model this situation.
a.) What do x and y represent?
b.) Graph the equation
c.) Write the equation in slope intercept form.
d.) What is the slope of the line?
e.) What does the slope tell you?
13. Write each equation in slope intercept form: 2x + 3y = 90
The solution provides detailed explanations of straight line equation such as its slope and intercept. It also shows how to graph the line.