Complete each ordered pair so that it satisfies the given equation.
7. y _ 3x _ 9: (0, ), ( , 24), (2, )
17. y = -2x+5
71. x - 3y - 6
Find the slope of each side
Graph the line with the given point and slope.
41. The line through (-2, 3) with slope - 2
51. Draw l1 through (-2,-3) and (4, 0). What is the slope of any line parallel to l1? Draw l2 through (1, 2) so that it is parallel to l1
Write an equation for each line. Use slope-intercept form if possible.
Find the slope and y-intercept for each line that has a slope and y-intercept
31. x - 2y= 4
Graph each line using its y-intercept and slope.
65. 4y + x= 8
In each case determine whether the lines are parallel, perpendicular, or neither.
69. y = 3x - 4
y = 3x - 9
Write each equation in slope-intercept form.
11. 3x - 4y = 80
Find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intercept form.
23. (-1, -7), -6
Find the equation of each line. Write each answer in slope intercept form.
55. The line is parallel to 2x + y = 8 and contains the point (-1, -3).
Find the equation of each line in the form y =mx + b if possible.
63. The line through (3, 2) and the origin
Write a formula that expresses the relationship described by each statement. Use k for the constant in each case.
5. T varies directly as h.
7. y varies inversely as r.
Find the variation constant, and write a formula that expresses the indicated variation.
17. A varies inversely as B, and A = 3 when B = 2.
Solve each variation problem.
25. Y varies directly as x, and Y = 100 when x = 20. Find Y when x = 5.
Discuss the necessary steps to solve for this problem.
64. 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 who retires at age 64? At what retirement age does a person receive an annual benefit of $11,600? Find the slope of each line segment on the graph, and interpret your results. Why do people who postpone retirement until 70 years of age get the highest benefit?
Solve for each problem
Decreasing price. World Auto uses the formula P = -3000n + 17,000 to determine the wholesale price
for a used Ford Focus, where P is the price in dollars and n is the age of the car in years. a) Find the price for a Focus that is 1, 2, or 3 years old. b) Find the slope and P-intercept for the line P = -3000n + 17,000. c) Interpret the slope and P-intercept.
94. 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.)
Provide a real-life application to demonstrate how to apply this concept.
Find the slope of the line through each pair of points.
1. (2, 5) and ( -2, 3)
2. (4, 1) and (6, -3)
Write the equation of each line described below. Give the answer in slope-intercept form
3. the line through (0, 5) with slope 4
4. the line through (4, -1) with slope 3/5
Sketch the graph of each equation
5. y = 2x -1
6. The line through (-1, -2) with slope 2/3
7. Graph this inequality
2x + y < 4
Solve each problem by writing and solving an equation.
96. World grain demand. Freeport McMoRan projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only ¾ of world grain demand.
What will world grain demand be in 2010?
Solve each problem
94. Fahrenheit temperature. Water boils at 212°F. a) Use the accompanying graph to determine the Celsius temperature at which water boils. b) Find the Fahrenheit temperature
70 = 5 (F _ 32).
96. Perimeter of a triangle. The perimeter of the triangle shown in the accompanying figure is 12 meters. Determine the values of x, x + 1, and x + 2 by solving the equation
x + (x + 1) + (x + 2) =12
Solve each equation
80. -3 - 4(t - 5) = - 2(t +3) + 11
88. 0.08x + 0.5(x + 100) = 73.2
94. Raising rabbits. Before Roland sold two female rabbits, half of his rabbits were female. After the sale, only one third of his rabbits were female. If x represents his original number of rabbits, then
Finding slope of a line by using slope intercept formula. Finding variables which are in direct or inverse variation to each other. Solving linear equtions.