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Questions and Answers of College Algebra

Determine whether each pair of lines is parallel, perpendicular, or neither.The line passing through (4, 6) and (-8, 7) and the line passing through (-5, 5) and (7, 4)
Write an equation in the form y = mx for each situation. Then give the three ordered pairs associated with the equation for x-values 0, 5, and 10.x represents the number of gallons of gas sold at
Determine whether each pair of lines is parallel, perpendicular, or neither.x + 4y = 7 and 4x - y = 3
Write an equation in the form y = mx for each situation. Then give the three ordered pairs associated with the equation for x-values 0, 5, and 10.x represents the number of hours a bicycle is rented
Determine whether each pair of lines is parallel, perpendicular, or neither.2x + 5y = -7 and 5x - 2y = 1
Determine whether each pair of lines is parallel, perpendicular, or neither.4x - 3y = 6 and 3x - 4y = 2
Write an equation in the form y = mx for each situation. Then give the three ordered pairs associated with the equation for x-values 0, 5, and 10.x represents the number of tickets to a performance
Determine whether each pair of lines is parallel, perpendicular, or neither.2x + y = 6 and x - y = 4
A ticket for Taylor Swift’s Reputation Stadium Tour costs $140. There is a ticket order delivery fee of $18.50. Let x represent the number of tickets and y represent the cost in dollars. How much
Think of ordered pairs of temperatures (C, F), where C and F represent corresponding Celsius and Fahrenheit temperatures. The equation that relates the two scales has a straight-line graph that
Determine whether each pair of lines is parallel, perpendicular, or neither.x = 6 and 6 - x = 8
A health club membership costs $99, plus $41 per month. Let x represent the number of months and y represent the cost in dollars. How much does the first year’s membership cost?(a) Write an
A wireless plan includes unlimited talk, text, and data for $90 per month. There is a $25 activation fee. Let x represent the number of months and y represent the cost in dollars. Over two years, how
Resident tuition at North Shore Community College is $206 per credit hour. There is also a $300 program fee for physical therapy. Let x represent the number of credit hours and y represent the cost
A wireless plan includes unlimited talk, text, and data for $75 per month. There is a $350 charge for a phone. Let x represent the number of months and y represent the cost in dollars. Over two
Determine whether each pair of lines is parallel, perpendicular, or neither.3x = y and 2y - 6x = 5
Determine whether each pair of lines is parallel, perpendicular, or neither.4x + y = 0 and 5x - 8 = 2y
An Executive VIP/Gold membership to a health club costs $159, plus $57 per month. Let x represent the number of months and y represent the cost in dollars. How much does a one-year membership
Determine whether each pair of lines is parallel, perpendicular, or neither.2x + 5y = -8 and 6 + 2x = 5y
Determine whether each pair of lines is parallel, perpendicular, or neither.4x - 3y = 8 and 4y + 3x = 12
Solve each problem. Give equations in slope-intercept form.Total sales of e-readers in the United States (in millions of dollars) are shown in the graph, where the year 2013 corresponds to x = 0.(a)
The upper deck at Guaranteed Rate Field in Chicago has produced, among other complaints, displeasure with its steepness. It is 160 ft from home plate to the front of the upper deck and 250 ft from
Solve each problem. Give equations in slope-intercept form.Total sales of smartphones in the United States (in billions of dollars) are shown in the graph, where the year 2013 corresponds to x =
When designing the TD Garden in Boston, architects designed the ramps leading up to the entrances so that circus elephants would be able to walk up the ramps. The maximum grade (or slope) that an
Expenditures for home health care in the United States are shown in the graph.(a) If a straight line were drawn through the tops of the bars for 2012 and 2016, would this line have positive or
Find and interpret the average rate of change illustrated in each graph. Value of Machine (in thousands of dollars) 1 Year 2 3 X + ∞0 12 16 200
Determine whether each pair of lines is parallel, perpendicular, or neither.2x = y + 3 and 2y + x = 3
There is a $30 fee to rent a chain saw, plus $6 per day. Let x represent the number of days the saw is rented and y represent the charge to the user in dollars. If the total charge is $138, for how
Determine whether each pair of lines is parallel, perpendicular, or neither.x = 6 and y = 4
A rental car costs $99, plus $0.50 per mile. Let x represent the number of miles driven and y represent the total charge to the renter in dollars. How many miles was the car driven if the renter paid
Determine whether each pair of lines is parallel, perpendicular, or neither.x + 1 = 0 and y - 2 = 0
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,A quick way to estimate Fahrenheit temperature for a given Celsius temperature is to double C and add 30. Use this
The graph shows the percent of households in the United States that were wireless-only households for the years 2011 to 2016.(a) In the context of this graph, what does the ordered pair (2016, 51)
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,Use the equation found in Exercise 101 and solve for C in terms of F. For what temperature does F = C ?Data from in
The graph shows the number of wireless subscriber connections (that is, active devices, including smartphones, feature phones, tablets, etc.) in millions in the United States for the years 2011 to
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,There is a linear relationship between Celsius and Fahrenheit temperatures. \ 40 30 20 0 -20 10 20 -30 -40 -40 10
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,Use the slope found in Exercise 100(b) and one of the two points determined earlier, and write an equation that
Find and interpret the average rate of change illustrated in each graph. Percent of Pay Raise y 8 9 2 01 2 3 4 Year X
Find and interpret the average rate of change illustrated in each graph. Amount Saved (in dollars) 400 300 200 100 01 2 3 Month + X
The number of pieces of first-class mail delivered in the United States is shown in the graph.(a) If a straight line were drawn through the tops of the bars for 2011 and 2016, would this line have
If the graph of a linear equation rises from left to right, then the average rate of change is (positive / negative). If the graph of a linear equation falls from left to right, then the average rate
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,Use the method given in Exercise 103 to estimate the Fahrenheit temperature given C = 30. Then use the equation from
The graph shows the number of U.S. travelers to Canada (in thousands) from 2000 through 2016.(a) Use the given ordered pairs to find the average rate of change in the number of U.S. travelers to
The graph shows the number of drive-in movie theaters in the United States from 2010 through 2017.(a) Use the given ordered pairs to find the average rate of change in the number of drive-in theaters
The average price of a gallon of unleaded gasoline in 2000 was $1.51. In 2016, the average price was $2.14. Find and interpret the average rate of change in the price of a gallon of gasoline per year
To see how the formula that relates Celsius and Fahrenheit temperatures is derived,Explain why the method given in Exercise 103 to estimate Fahrenheit temperature gives a good approximation ofData
Three points that lie on the same straight line are said to be collinear. Consider the points A(3, 1), B(6, 2), and C(9, 3).Use the slope formula to determine whether the points (1, -2), (3, -1), and
Three points that lie on the same straight line are said to be collinear. Consider the points A(3, 1), B(6, 2), and C(9, 3).If slope of segment AB = slope of segment BC = slope of segment AC, then A,
Three points that lie on the same straight line are said to be collinear. Consider the points A(3, 1), B(6, 2), and C(9, 3).Find the slope of segment AC.
Three points that lie on the same straight line are said to be collinear. Consider the points A(3, 1), B(6, 2), and C(9, 3).Find the slope of segment BC.
Three points that lie on the same straight line are said to be collinear. Consider the points A(3, 1), B(6, 2), and C(9, 3).Find the slope of segment AB.
Use your knowledge of the slopes of parallel and perpendicular lines.Is the figure with vertices at (-11, -5), (-2, -19), (12, -10), and (3, 4) a parallelogram? Is it a rectangle?
Use your knowledge of the slopes of parallel and perpendicular lines.Show that (-13, -9), (-11, -1), (2, -2), and (4, 6) are the vertices of a parallelogram.
In 2010, worldwide shipments of desktop computers totaled 157 million units. In 2016, 103 million units were shipped. Find and interpret the average rate of change in worldwide shipments of desktop
In 2010, the number of digital cameras shipped worldwide totaled 122 million. There were 24 million shipped in 2016. Find and interpret the average rate of change in the number of digital cameras
The average price of a movie ticket in 2004 was $6.21. In 2016, the average price was $8.65. Find and interpret the average rate of change in the price of a movie ticket per year to the nearest cent.
Write an equation of the line passing through the given points. Give the final answer in standard form. 2 (-12, -3) and (-3, -3) 2²
Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for a problem such as the following. A factory can have no more than 200 workers on a
Graph each linear or constant function. Give the domain and range. F(x) = 1 4 x + 1
Write an equation of the line passing through the given points. Give the final answer in standard form. (13, 5) and (13, -1)
Graph each linear or constant function. Give the domain and range. 1 h(x) = -x + 2 2
Write an equation of the line passing through the given points. Give the final answer in standard form. (7, 6) and (7,-8)
Find the x-and y-intercepts. Then graph each equation.x - 4 = 0
Write an equation of the line passing through the given points. Give the final answer in standard form. (-2, 2) and (4, 2)
Find the slope of each line, and sketch its graph.x + 3y = -6
Graph the union of each pair of inequalities. x-y≥1 or x + y ≤ 4
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.x = y4
Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for a problem such as the following. A factory can have no more than 200 workers on
Find the x-and y-intercepts. Then graph each equation.x + 4 = 0
Find the slope of each line, and sketch its graph.x + 2y = 4
Graph the union of each pair of inequalities. 3x + 2y < 6 or x - 2y > 2
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.x = y6
Graph each linear or constant function. Give the domain and range.g(x) = 4x - 1
Write an equation of the line passing through the given points. Give the final answer in standard form. (2, 5) and (1,5)
Find the x-and y-intercepts. Then graph each equation.x = -3
Write an equation of the line passing through the given points. Give the final answer in standard form. (-2, 5) and (-8, 1)
Graph the union of each pair of inequalities. x + 3y or x > 3
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.y = x3
Find the slope of each line in three ways by doing the following.(a) Give any two points that lie on the line, and use them to determine the slope.(b) Solve the equation for y, and identify the slope
Write an equation of the line passing through the given points. Give the final answer in standard form. (6, 1) and (-2, 5)
Graph each linear or constant function. Give the domain and range.ƒ(x) = -2x + 5
Find the x-and y-intercepts. Then graph each equation.x = 2
Graph the union of each pair of inequalities. x-2y or x < 1
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.y = x2
Find the slope of each line in three ways by doing the following.(a) Give any two points that lie on the line, and use them to determine the slope.(b) Solve the equation for y, and identify the slope
Find the x-and y-intercepts. Then graph each equation. 3 4 y = x
Graph the union of each pair of inequalities. x + y ≤2 or y ≥ 3
Find the x-and y-intercepts. Then graph each equation.y = -3
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.y = 6x + 8
Find the slope of each line in three ways by doing the following.(a) Give any two points that lie on the line, and use them to determine the slope.(b) Solve the equation for y, and identify the slope
Find the x-and y-intercepts. Then graph each equation.y = 5
Find the x-and y-intercepts. Then graph each equation. 2 I y = x 3-
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.y = 2x - 6
Find the slope of each line in three ways by doing the following.(a) Give any two points that lie on the line, and use them to determine the slope.(b) Solve the equation for y, and identify the slope
Write an equation of the line passing through the given points. Give the final answer in standard form. (5,-2) and (-3, 14)
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.y = -9x
Find the slope of each line in three ways by doing the following.(a) Give any two points that lie on the line, and use them to determine the slope.(b) Solve the equation for y, and identify the slope
Use the definition of absolute value to write each inequality as a compound inequality, and graph its solution set in the rectangular coordinate plane. |y3|
Graph the union of each pair of inequalities. x y1 or y ≥ 2
Write an equation of the line passing through the given points. Give the final answer in standard form. (3, 4) and (5,8)

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