Question 1

Provide an appropriate response.
-Without making a drawing, explain why the graph of the equation y = x - 5 passes through three quadrants.

Accepted Answer

The answer of Provide an appropriate response.
-Without making a drawing,...

Question 2

Solve the problem.
-Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 789. Find a linear function, S(t), which fits this data, And which expresses score as a function of time. Use this function to predict an average score for persons taking A 58-hour review course. Round your answer to the tenths place.
A)738.3
B)752.3
C)742.5
D)731.0

Accepted Answer

The linear function can be found using the two given points: (30, 620) and (70, 789). The slope (m) is calculated as (789-620)/(70-30) = 169/40 = 4.225. Using one of the points to find the y-intercept (b), we get 620 = 4.225(30) + b, leading to b = 493.25. Thus, the linear function is S(t) = 4.225t + 493.25. Substituting t = 58, S(58) = 4.225(58) + 493.25 = 738.25, which rounds to 738.3.

Question 3

Solve the problem.
-A gas station sells 4820 gallons of regular unleaded gasoline on a day when they charge $1.35 per gallon, whereas they sell 3850 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses
Gallons sold as a function of price.
A)G(p)= -19,400p + 30,988.2
B)G(p)= -19,400p + 31,026
C)G(p)= -19,400p + 31,010
D)G(p)= -19,400p + 30,993.8

Accepted Answer

The answer of Solve the problem.
-A gas station sells 4820...

Question 4

Solve the problem.
-In 1995 the United States recovered 25% of its municipal solid wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Find a linear function P(t)that fits
This data.
A)P(t)= -1.6t + 7
B)P(t)= 0.8t - 17
C)P(t)= 1.6t + 17
D)P(t)= 1.6t + 24

Accepted Answer

The linear function that fits the data is found by determining the slope (change in percentage per year) and the y-intercept (percentage at year 0, which is 1990 in this context). The slope is $\frac{25\% - 17\%}{1995 - 1990} = \frac{8}{5} = 1.6$. Since at $t = 0$ (year 1990), $P = 17\%$, the equation is $P(t) = 1.6t + 17$.

Question 5

Provide an appropriate response.
-Why is the slope of a horizontal line zero?

Accepted Answer

The answer of Provide an appropriate response.
-Why is the slope...

Question 6

Provide an appropriate response.
-The total number of reported cases of AIDS in the United States has risen from 372 in 1981 to 100,000 in 1989 and 200,000 in 1992. Does a linear equation fit this data? Why or why not?

Accepted Answer

The answer of Provide an appropriate response.
-The total number of...

Question 7

Solve the problem.
-A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3958 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses
Gallons sold as a function of price. Use this function to predict the number of gallons sold at a price of $1.21 per
Gallon.
A)7242.6 gallons
B)7237.7 gallons
C)7233.6 gallons
D)7230.3 gallons

Accepted Answer

The answer of Solve the problem.
-A gas station sells 4820...

Question 8

Provide an appropriate response.
-Can an equation of a vertical line be written in slope-intercept form?

Accepted Answer

the slope of a vertical line is undefined.

Question 9

Solve the problem.
-Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 765. Find a linear function S(t), which fits this data,
And which expresses score as a function of time.
A)S(t)= 3.625t + 511.25
B)S(t)= 3.2625t - 515.25
C)S(t)= -3.625t + 511.25
D)S(t)= 3.2625t + 515.25

Accepted Answer

To find a linear function $S(t) = mt + b$, we use the given points (30, 620) and (70, 765). The slope $m$ is calculated as $\frac{765 - 620}{70 - 30} = \frac{145}{40} = 3.625$. To find $b$, we can use one of the points: $620 = 3.625(30) + b$, solving for $b$ gives $b = 620 - 108.75 = 511.25$. Thus, the function is $S(t) = 3.625t + 511.25$.

Question 10

Provide an appropriate response.
-Describe a situation in which point-slope form would be more useful.

Accepted Answer

The answer of Provide an appropriate response.
-Describe a situation in...

Question 11

Provide an appropriate response.
-Can the point-slope equation be used to write an equation of a vertical line? Why or why not?

Accepted Answer

the slope of a vertical line is undefined.

Question 12

Provide an appropriate response.
-If one line has a slope of -3 and another line has a slope of -6, which line is steeper? Why?

Accepted Answer

The answer of Provide an appropriate response.
-If one line has...

Question 13

Provide an appropriate response.
-Explain why the order in which coordinates are subtracted to find slope does not matter as long as
x-coordinates are subtracted in the same order as y-coordinates.

Accepted Answer

The answer of Provide an appropriate response.
-Explain why the order...

Question 14

Solve the problem.
-In 1995 the United States recovered 22% of its municipal wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Find a linear function P(t)that fits this
Data. Use this function to predict the percentage recycled in 2002.
A)30.7%
B)25.4%
C)29%
D)27.1%

Accepted Answer

The answer of Solve the problem.
-In 1995 the United States...

Question 15

Provide an appropriate response.
-Explain in your own words why equations of the form y = b have graphs that are horizontal lines.

Accepted Answer

The answer of Provide an appropriate response.
-Explain in your own...

Question 16

Write an equation of the line described.
-Through (-4, 5), perpendicular to x = -2
A)y = 5
B)y = -5
C)y = -4x + 5
D)y = -4

Accepted Answer

The line x = -2 is a vertical line. A line perpendicular to a vertical line is a horizontal line, which has an equation of the form y = k, where k is the y-coordinate of any point the line passes through. Since the line passes through (-4, 5), the equation is y = 5.

Question 17

Provide an appropriate response.
-Why is the slope of a vertical line undefined?

Accepted Answer

The answer of Provide an appropriate response.
-Why is the slope...

Question 18

Solve the problem.
-The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total sales after 28 months.
A)$78,792
B)$78,720
C)$78,850
D)$78,750

Accepted Answer

The sales increase can be modeled linearly. The increase from 3 to 23 months is $43,000 ($68,000 - $25,000), over 20 months. This gives a monthly increase of $2,150 ($43,000/20). From 23 to 28 months is 5 months, so the increase is $10,750 (5 * $2,150). Adding this to $68,000 gives $78,750.

Quiz 7: Graphs, Functions, and Applications

Provide an appropriate response. -Without making a drawing, explain why the graph of the equation y = x - 5 passes through three quadrants.

Solve the problem. -A gas station sells 4820 gallons of regular unleaded gasoline on a day when they charge $1.35 per gallon, whereas they sell 3850 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses Gallons sold as a function of price.

Solve the problem. -In 1995 the United States recovered 25% of its municipal solid wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Find a linear function P(t) that fits This data.

Provide an appropriate response. -Why is the slope of a horizontal line zero?

Provide an appropriate response. -The total number of reported cases of AIDS in the United States has risen from 372 in 1981 to 100,000 in 1989 and 200,000 in 1992. Does a linear equation fit this data? Why or why not?

Provide an appropriate response. -Can an equation of a vertical line be written in slope-intercept form?

Solve the problem. -Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 765. Find a linear function S(t) , which fits this data, And which expresses score as a function of time.

Provide an appropriate response. -Describe a situation in which point-slope form would be more useful.

Provide an appropriate response. -Can the point-slope equation be used to write an equation of a vertical line? Why or why not?

Provide an appropriate response. -If one line has a slope of -3 and another line has a slope of -6, which line is steeper? Why?

Provide an appropriate response. -Explain why the order in which coordinates are subtracted to find slope does not matter as long as x-coordinates are subtracted in the same order as y-coordinates.

Provide an appropriate response. -Explain in your own words why equations of the form y = b have graphs that are horizontal lines.

Write an equation of the line described. -Through (-4, 5) , perpendicular to x = -2

Provide an appropriate response. -Why is the slope of a vertical line undefined?

Solve the problem. -The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total sales after 28 months.