algebra 1a - unit 2: lines and their graphs

what is the correct slope-intercept form of the equation 3x − 11y = −22?

y = 3/11x + 2

examine the following graph of -1/2x - 8. which of the following points are on this line? select all that apply.

(-8, -4) (-4, -6) (-16, 0)

each day, a factory produces a total of 280 containers of ice cream. the flavors are vanilla, chocolate, and strawberry. each day, the factory produces twice as much chocolate ice cream as strawberry ice cream and 20 more containers of vanilla ice cream than strawberry ice cream. what is the correct equation, and what is the correct solution, for this situation, where s represents the number of containers of strawberry ice cream produced per day?

correct equation: 280 = s + 2s + s + 20 correct solution: the factory produces 65 containers of strawberry ice cream per day.

examine the following line. https://cdstools.flipswitch.com/asset/media/934141 which equation correctly represents the line in point-slope form?

y - 3 = 1/2(x + 3)

a manager measured the number of goods, y, that his company produced in x hours. the company produces goods at a rate of 5 per hour. at hour 9, the company had produced 45 goods. which equation, in point-slope form, correctly represents the goods produced by the company after x hours?

y - 45 = 5(x - 9)

the total cost for wally to operate his hot dog stand is represented in the following graph. which equations correctly represent wally's cost over time?

y - 51 = 3/4(x - 8) y - 48 = 3/4(x - 4)

solve for x: 3(x - 2) = 9

5

mimi opened a savings account to save money to go on a vacation this summer. her savings are displayed in the following table, which can be represented with a line. which answer correctly explains how to graph the line for this situation?

plot the starting point (0, 210) and any other point from the table, such as (4, 430). draw a line from (0, 210) through the point (4, 430). label the x-axis as "months since opening account" and the y-axis as "amount saved (dollars)." use a 1-month scale for the x-axis and a 100-dollar scale for the y-axis.

which statement is true?

the graph of a two-variable equation is the set of all points in the coordinate plane that solve the equation.

which graph correctly shows the x- and y-intercepts of the line represented by the equation 2x + 5y = 18?

https://cdstools.flipswitch.com/asset/media/935323

match each equation with the correct value of t that makes the equation true.

3t - 1/4 = 0.75 : t = 1/3 -2/5t + 6 = 14 : t = -20 t+0.5/2 = 7.25 : t = 14 t ÷ 9 + 5 = 50 : t = 405

lesson 6

solving linear equations

the following graph shows the system of equations {20x - 25y = 11, 2x + 3y = 11}. what is the approximate solution for the system of equations?

(2.8, 1.8)

examine the following graph of y = 1/4x + 2. if the point (-4, b) is on the line, what is the value of b?

1

consider the equation y − 2 = 3(x + 2). which option correctly identifies the point and slope from the equation and also provides the graph that correctly represents the equation?

https://cdstools.flipswitch.com/asset/media/935293

match each graph with the correct number of solutions.

no solution : https://cdstools.flipswitch.com/asset/media/934606 one solution : https://cdstools.flipswitch.com/asset/media/934607 infinitely many solutions : https://cdstools.flipswitch.com/asset/media/934608

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/939515 which equation, in point-slope form, correctly represents the line in the graph?

y + 4 = 2(x - 7)

what is the point-slope form of the equation for the line with a slope of −2 that passes through the point (4, −6)?

y + 6 = -2(x - 4)

brooke is reading a 379-page book. she has already read 54 pages, and she can read 28 pages in an hour. if h represents the number of hours it will take brooke to read the book, which equation models this situation?

28h + 54 = 379

which graph correctly shows the system of equations {y = 1/2x + 2, y = -1/2x + 6}?

https://cdstools.flipswitch.com/asset/media/934465

the graph of y = 5/4x + 1 is shown below. what is the value of the y-coordinate?

1

lesson 7

forms of equations of lines

lesson 8

graphing lines

examine the following table that represents some points on a line. what is the slope-intercept form of the equation for this line?

y = 2/5x - 1/5

what is the correct slope-intercept form of the equation y + 4 = 2(x − 3)?

y = 2x - 10

what is the correct slope-intercept form of the equation y + 16 = 3(x − 0)?

y = 3x - 16

lesson 9

creating linear equations from graphs

the following table contains some of the ordered pairs of a linear relationship between the number of hours that have passed since a pool began to drain and the amount of water in gallons in the pool. which graph correctly represents this linear relationship?

https://cdstools.flipswitch.com/asset/media/931814

consider the equation y + 13 = -7/2(x - 4). which answer correctly identifies the point and slope from the equation and also provides the graph that correctly represents the equation?

https://cdstools.flipswitch.com/asset/media/932154

which graph correctly shows the x- and y-intercepts of the line represented by the equation 9x + 2y = 15?

https://cdstools.flipswitch.com/asset/media/932397

which graph correctly shows the system of equations {x - 2y = 4, y = 2x + 4}?

https://cdstools.flipswitch.com/asset/media/934474

which graph correctly shows the system of equations {x - 2y = -7, -4x + y = 14}?

https://cdstools.flipswitch.com/asset/media/934482

a game store sells 2 large puzzles for $16 and 3 small puzzles for $15. the store made $128 in puzzle sales this week. the equation 8l + 5s = 128 represents this week's earnings from puzzle sales, where l represents the number of large puzzles sold and s represents the number of small puzzles sold. which statements are correct regarding the equation 8l + 5s = 128? select all that apply.

the coefficient 8 in the equation gives the cost of one large puzzle. the coefficient 5 in the equation gives the cost of one small puzzle.

at her track practice, marcella can run at 2.4 meters per second. she writes the equation y = 2.4x to represent how many meters she runs after a certain number of seconds. which statement is true regarding the variables in the equation y = 2.4x?

the dependent variable, y, is the number of meters marcella runs. the independent variable, x, is the number of seconds marcella runs.

sherlene bought 3 pounds of coffee and 2 pounds of chocolate for a total of $24. which equation, written in standard form, correctly represents this scenario and correctly indicates what the variables represent?

the correct equation is 3x + 2y = 24, where x is the price per pound of coffee and y is the price per pound of chocolate.

examine the following table, which represents some points on a line. what is the equation for the line in slope-intercept form?

y = -1/3x - 2

a line passes through the points (-2, 15/2) and (1/8, -1). what is the slope-intercept form of the equation for this line?

y = -4x - 1/2

leo and bonnie went to watch the local basketball team's game. each of them bought a game ticket and a $15 team jersey. together, they paid a total of $70.50. how much was each ticket?

$20.25

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/934082 what is the slope of the line?

-2/3

what value of x makes the following equation true? 6x = 3/22

1/44

ahmet rents a piano for $35 per month. he earns $25 per hour giving piano lessons to students. he wants to know how many hours of lessons per month he must give to earn a profit of $440. which answer describes the correct solution for the situation?

it will take 19 hours of lessons

a plane is flying to metro city. the plane started its journey 1275 miles from metro city. write an equation in standard form to represent the situation if the plane travels aa hours at 550 mph and b hours at 590 mph. which equation is correctly written in standard form to represent this scenario?

550a + 590b = 1275

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/939495 what is the slope of the line in the graph?

1/2

in a given year, the population of metro city is 7420, and the population is decreasing by 152 people per year. the population of smallville is consistently 1200 less than half of metro city. determine how long it will take for smallville's population to reach 2282. which answer provides the correct equation and solution for the situation, where x represents the number of years?

the equation is 2282 = 12(7420 − 152x) − 1200. it will take 3 years for the population of smallville to be 2282 people.

use the scenario to answer the question. an egg farmer determined that it costs him $0.05 per egg to harvest chicken eggs. in addition, he spends $1000 each month for the upkeep of his farm. write an equation in slope-intercept form that represents the monthly cost of the farm in dollars, y, when it produces x eggs. which answer correctly identifies the slope and equation for this situation?

the slope is 0.05 because this is the cost per egg. the equation is y = 0.05x + 1000.

examine the following graph of -3x + 2y = 6. which of the following pairs are on this line? select all that apply.

(2, 6) (-4, -3) (-6, -6)

which method represents a correct way to solve the equation 2(t − 5) = 48?

2(t - 5) = 48 t - 5 = 24 t = 29

kevin will graph the line represented by the equation x − 6y = 18. he first plotted the x- and y-intercepts as follows. which statement is true regarding the intercepts on the graph?

kevin incorrectly plotted the intercepts. he should have switched the coordinates of the points to have the x-intercept at (18, 0) and the y-intercept at (0, −3).

zuzana graphed a line using the equation y = −x + 1 as follows. zuzana made two mistakes. select all true statements.

she incorrectly graphed the line by using a slope of 1 instead of −1. she incorrectly graphed the y-intercept at (0, −1) instead of at (0, 1).

alex and his father took a taxi cab that charges $2.60 per mile plus $1.50 for each passenger, and they paid a total of $$18.60. alex wrote the equation 18.60 = 2.60b + 3 for this situation and found b = 6. which statement is true about the solution b = 6?

the solution b = 6 gives the number of miles the taxi traveled.

what is the solution to the equation 4x − 2 = 18?

x = 5

klara's solution to the equation −5x − 8 = 32 is as follows. step 1: −5x = 40 step 2: x = −8x which property did klara use for step 2?

division property of equality

kenji and antwan have jobs that pay differently. antwan gets paid an hourly wage of $20. kenji gets paid an hourly wage of $15 and receives $35 a day in tips. both men worked h hours on tuesday and earned the same amount of money. if the equation 20h = 15h + 35 models this situation, how many hours did each man work?

each worked 7 hours

which statement is true about the line represented by the equation y + 7 = -3(x - 2/9)?

the point (2/9, -7) is on the line.

during a trip, amy had to take two different trains. her first train traveled for 3 hours, and the second train traveled for 4 hours. combined, the trains traveled 625 miles. if the equation 3m + 4n = 625 represents this situation, which statements are true regarding this equation?

the variable m in the equation represents the speed of the first train. the variable n in the equation represents the speed of the second train.

the following graph shows a system of equations. which point is a solution for the system?

(2, 2)

the heights of two trees were measured over several years. the measurements are shown in the following graph for the system of equations, where the x-axis shows the time in years and the y-axis shows the height in feet. after _[blank a]_ years, both trees are _[blank b]_ feet tall. what values correctly complete the previous sentence?

blank a: 5 blank b: 12

which graphs show a system of equations with no solution? select all that apply.

https://cdstools.flipswitch.com/asset/media/934594 https://cdstools.flipswitch.com/asset/media/934592

which graph shows a system of equations with infinitely many solutions?

https://cdstools.flipswitch.com/asset/media/934601

at an elementary school, the fourth-grade class is planning a field trip to the science center. the roster shows 113 students who will attend the event. school-district rules specify the there must be one adult chaperone for every 10 students. which equations correctly represent this situation, where c is the number of chaperones? select all that apply.

10c = 113 c = 113/10

lesson 10

solving linear systems by graphing

the following graph shows the system of equations {2x + 3y = 9, y = x + 8}. what is the solution for the system of equations?

(-3,5)

ezgi's mom took ezgi and her five friends to the circus for her birthday party. her mom got a $12.50 ticket and the same snack for each child from the concession stand. she paid $105 for all of the tickets and snacks. which equations represent this situation, where s represents the cost of one snack in dollars? select all that apply.

6s + 75 = 105 6(s + 75) = 105

examine the following graph of y = −3x + 7. match each x-coordinate with the corresponding y-coordinate.

x-coordinate = 0 : y-coordinate = 7 x-coordinate = 2 : y-coordinate = 1 x-coordinate = 3 : y-coordinate = -2 x-coordinate = 5 : y-coordinate = -8

examine the following line. https://cdstools.flipswitch.com/asset/media/934102 what is the y-intercept of the line?

(0, -2)

amira is told there is a trick to finding the slope within an equation in standard form. she is told she can rewrite this equation in slope-intercept form, to find the pattern. she correctly rewrites the equation 7x + 9y = 14 in slope-intercept form as y = -7/9x + 14/9. which answer explains the pattern for how to find the slope using an equation in standard form?

in slope-intercept form, the slope is −7/9. these values are a and b, but with the opposite sign, so the slope of the line from the equation in standard form is −a/b.

examine the situation. mr. mauldin has twice as many students as mrs. sasser and mr. khan combined. if mr. mauldin has 35 students, and mrs. sasser has 9, how many students does mr. khan have? tim represents this situation with the equation 35 = 2(9 + k), where k represents the number of students mr. khan has. tim found the answer to be 8.5. which statement is true about tim's solution to the problem?

the value 8.5 is the correct solution to the equation, but it is not reasonable, because there can't be 8.5 students in a class. this means the problem's situation can't be true.

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/934105 which answer choice correctly identifies key features of the line and the correct equation for the line in slope-intercept form?

the y-intercept is the point (0, 11) and the line has a slope of −1/4. therefore, the equation is y = −1/4x + 11.

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/939507 which answer correctly identifies key features of the line and the correct equation for the line in slope-intercept form?

the y-intercept is the point (0, 5) and the line has a slope of 54. therefore, the equation is y = 5/4x + 5.

carmella filled her swimming pool. before she started to fill it, there was already some water inside the pool. the water entered the pool at the same amount each hour. the following table shows how much water was inside the pool at various times after carmella started to fill it. what could the appropriate labels be for the x-axis and y-axis when correctly graphing the line for this situation? match each axis with the appropriate label.

x-axis : 1-hour intervals y-axis : 1000-gallon intervals

what is the slope of the line that is represented by the equation y - 1/5 = -6(x + 7)?

-6

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/934089 what is the slope of the line?

1/8

valerie took a day-trip. she drove from her house for a while and took a coffee break. after her coffee break, she continued driving. after 2 hours of driving after her coffee break, her distance from her house was 210 miles. her average speed during the whole trip was 60 miles per hour. valerie created the equation y − 210 = 60(x − 2) to represent this situation, where x represents the time in hours from her coffee break and y represents the distance in miles from her house. which graph correctly represents Valerie's distance from her house after her coffee break?

https://cdstools.flipswitch.com/asset/media/932177

officer franklin is on traffic duty. his motorcycle is parked alongside the freeway, and he's using his radar gun to check the speed of cars. a sports car races by officer franklin, causing him to lose his grip on the radar gun. when he picks it back up, he clocks the car at 93 miles per hour as it passes a bridge one-half of a mile ahead of him. the equation d = 93h + 1/2 represents the distance of the sports car in miles from the police officer, d, where h represents the time in hours traveled. which graph correctly represents this situation?

https://cdstools.flipswitch.com/asset/media/932290

which graph correctly represents the equation y = −4x − 3?

https://cdstools.flipswitch.com/asset/media/932340

which graph correctly shows the x- and y-intercepts of the line represented by the equation −x + 4y = −12?

https://cdstools.flipswitch.com/asset/media/932378

one year of membership at a rec center includes a fixed monthly cost and a one-time membership fee. the following table contains some of the ordered pairs for this linear relationship between the number of months enrolled and the total cost paid for the membership. which graph correctly represents this linear relationship?

https://cdstools.flipswitch.com/asset/media/935246

which graph correctly represents the equation y = −5/3x + 6?

https://cdstools.flipswitch.com/asset/media/935309

jacob is graphing the line represented by the equation −6x − 5y = 12. he first plots the x- and y-intercepts as follows. which statement is correct regarding the intercepts on the graph?

jacob incorrectly plotted the intercepts. he should have switched the coordinates of the points to have the x-intercept at (−2, 0) and the y-intercept at (0, −2.4).

maritza, kerstin, and hermine are collecting books. maritza has twice as many books as kerstin. hermine has 15 fewer books than kerstin. the three girls have 113 books in all. how many books does kerstin have? which answer shows the correct equation, as well as correct answer to the question, for this situation, where m represents the number of books that maritza has?

the equation is m + 1/2m + (1/2m - 15) = 113. kerstin has 32 books

teah was selling candy bars for a fundraiser. she spent $25 on a box of candy bars and sold each candy bar for $2.50. her profit was $75. teah wrote the equation 2.5c − 25 = 75 for this situation, and she found c = 40. which statement is true about the solution c = 40?

the solution c = 40 is the number of candy bars teah sold.

examine the situation. sermet needs $3250 and has already saved $1000. he thinks he can earn the rest of the money by working for one week at a bookstore that will pay him $12.50 per hour. sermet created the equation 3250 = 12.5h + 1000 to determine how many hours he needs to work at the bookstore in one week, and he found h = 180 hours. which statement is true about sermet's solution to the problem?

the value 180 is the correct solution to the equation, but it is not reasonable. since there are only 168 hours in a week, it is not possible for him to make enough money in one week.

a taxi cab charges a fixed amount per mile, plus $2.50 for two people. the following table shows some data for the relationship between the total cost for two people to take the taxi and the number of miles driven. in order to graph the line for this relationship, including the points from the table, what are the appropriate scales for the x-axis and y-axis? match each axis with the appropriate scale.

x-axis : 1-mile intervals y-axis : 5-dollar intervals

examine the following table, which represents some points on a line. which equations in point-slope form represent this line? select all that apply.

y + 6 = 2(x + 3) y - 2 = 2(x - 1) y - 4 = 2(x - 2)

examine the following table that represents some points on a line. which equations in point-slope form represent this line? select all that apply.

y + 9 = 1/2(x + 4) y + 4 = 12(x − 6) y + 10 = 12(x + 6)

zada is paid an hourly rate, as well as a bonus, each day. her hourly rate is $12 per hour. when she works 4 hours, she earns a total of $68. which equation, in point-slope form, correctly represents zada's pay in dollars, y, when she works x hours?

y - 68 = 12(x - 4)

what is the point-slope form of the equation for the line with a slope of 6/19 that passes through the point (-1, 7/5)?

y - 7/5 = 6/19(x + 1)

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/939512 which equation correctly represents the line in slope-intercept form?

y = 1/4x - 6

the slope of a line is 5/8, and the line passes through the point (-8, -4). what is the slope-intercept form of the equation for this line?

y = 5/8x + 1

examine the following graph of a line. https://cdstools.flipswitch.com/asset/media/934113 what is the slope-intercept form of the equation of the line?

y = 6x + 2