Question 1

A sales representative of a company using a personal car receives $160 per day for lodging and meals plus $0.53 per mile driven.Select a linear equation giving the daily cost C to the company in terms of x, the number of miles driven.  
A) $C = 0.53 + 160 x$
B) $C = 0.53 x + 160$
C) $C = - 0.53 x - 160$
D) $C = 0.53 x - 160$
E) $C = - 0.53 x + 160$

Accepted Answer

The correct equation is $C = 0.53x + 160$, where $0.53 per mile is the variable cost per mile driven (x), and $160 is the fixed daily cost for lodging and meals.

Question 2

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is  
  $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$  
X-intercept: (-3, 0)
Y-intercept: (0, 8)

A) $- 3 x + 8 y + 24 = 0$
B) $8 x + 3 y + 24 = 0$
C) $8 x - 3 y + 24 = 0$
D) $8 x - 3 y - 24 = 0$
E) $- 3 x + 8 y - 24 = 0$

Accepted Answer

The answer of Use the intercept form to find the...

Question 3

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is   $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$  
 
X-intercept: ( $- \frac { 5 } { 8 }$ , 0)
Y-intercept: $( 0 , - 3 )$ 
 
A) $- 24 x - 8 y - 5 = 0$
B) $24 x + 8 y - 5 = 0$
C) $- 24 x + 8 y + 5 = 0$
D) $24 x + 5 y + 15 = 0$
E) $24 x - 8 y + 5 = 0$

Accepted Answer

The answer of Use the intercept form to find the...

Question 4

A school district purchases a high-volume printer, copier, and scanner for $20,000. After 10 years, the equipment will have to be replaced.Its value at that time is expected to be $2,600.Select a linear equation giving the value of the equipment during the 10 years it will be in use.
 
A) $V = 1740 t - 20,000$
B) $V = - 1740 t - 20,000$
C) $V = 1740 t + 20,000$
D) $V = - 1740 t + 20,000$
E) $V = - 1740 + 20,000 t$

Accepted Answer

The value of the equipment decreases linearly from $20,000 to $2,600 over 10 years, which is a decrease of $17,400. Dividing this decrease by the time period gives a rate of decrease of $1,740 per year. Therefore, the value $V$ at time $t$ (in years) can be represented by starting value minus the depreciation over time: $V = 20,000 - 1,740t$, which rearranges to $V = - 1,740t + 20,000$.

Question 5

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = 134.
​
A)No change in sales
B)Sales decreasing 134 units/yr
C)Sales increasing 134 units/yr
D)None of the above

Accepted Answer

The slope of the line represents the rate of change of annual sales with respect to time. Since the slope is positive (134), it means that for every one-year increase in time, the annual sales increase by 134 units. So, the correct choice is C, sales increasing 134 units/yr.

Question 6

A sub shop purchases a used pizza oven for $885.After 5 years, the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use.  
A) $V = - 177 + 885 t$
B) $V = - 177 t - 885$
C) $V = 177 t - 885$
D) $V = 177 t + 885$
E) $V = - 177 t + 885$

Accepted Answer

The correct equation is $V = - 177 t + 885$. This is because the oven depreciates linearly over 5 years, losing $177 in value each year (885/5 = 177), starting from an initial value of $885.

Question 7

Estimate the slope of the line. ​  ​
A)-2
B)-3
C)-4
D)-1
E)Undefined

Accepted Answer

The answer of Estimate the slope of the line. ​...

Question 8

Determine whether the lines are parallel, perpendicular, or neither.  
L1: y = $\frac { 1 } { 2 }$ x - 4
L2: y = - $\frac { 1 } { 2 }$ x - 2
 
A)Parallel
B)Perpendicular
C)Neither

Accepted Answer

The answer of Determine whether the lines are parallel, perpendicular,...

Question 9

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is  
  $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ 
X-intercept: $\left( - \frac { 1 } { 6 } , 0 \right)$ y-intercept: $\left( 0 , - \frac { 2 } { 7 } \right)$  
 
A) $12 x - 7 y + 2 = 0$
B) $- 12 x + 7 y + 2 = 0$
C) $12 x + 7 y + 2 = 0$
D) $- 7 x - 12 y - 2 = 0$
E) $12 x + 7 y - 2 = 0$

Accepted Answer

The answer of Use the intercept form to find the...

Question 10

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = -20.
​
A)Sales increasing 20 units/yr
B)Sales decreasing 20 units/yr
C)No change in sales
D)None of the above

Accepted Answer

The negative slope (-20) indicates a decrease in sales. Specifically, for each increase of one year in time, sales decrease by 20 units.

Question 11

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​
The line has a slope of m = 500.
​
A)Revenues increasing 500 units/day
B)No change in revenues
C)Revenues decreasing 500 units/day
D)None of the above

Accepted Answer

The slope of 500 represents a daily increase of $500 in revenue for each additional day. Therefore, for a one-day increase in time, the daily revenue would increase by $500.

Question 12

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $\frac { 5 } { 100 }$ .Approximate the amount of vertical change in your position if you drive 400 feet.  
A)18 ft
B)21 ft
C)22 ft
D)19 ft
E)20 ft

Accepted Answer

The slope of the road is given as 5%, which means for every 100 feet horizontally, there is a 5 feet vertical change. For 400 feet, the vertical change is $400 \times \frac{5}{100} = 20$ feet.

Question 13

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ 
 Point on line: (4, 6)
X-intercept: (c, 0)
Y-intercept: (0, c), c$\neq$ 0

A) $x + y + 10 = 0$
B) $x + y - 10 = 0$
C) $- x + y - 10 = 0$
D) $x - y - 10 = 0$
E) $- x - y - 10 = 0$

Accepted Answer

Given the intercepts are (c, 0) and (0, c), the intercept form equation is $\frac{x}{c} + \frac{y}{c} = 1$, which simplifies to $x + y = c$. Since the point (4, 6) lies on the line, substituting x = 4 and y = 6 gives $4 + 6 = c$, so $c = 10$. Therefore, the equation is $x + y - 10 = 0$.

Question 14

A microchip manufacturer pays its assembly line workers $12.25 per hour.In addition, workers receive a piecework rate of $0.3 per unit produced.Select a linear equation for the hourly wage W in terms of the number of units x produced per hour.  
A) $W = 0.3 x + 12.25$
B) $W = 0.3 x - 12.25$
C) $W = 12.25 x + 0.3$
D) $W = 12.25 x - 0.3$
E) $W = 12.55 x$

Accepted Answer

The hourly wage W consists of a fixed hourly rate ($12.25) plus a variable piecework rate ($0.3 per unit), so the equation is $W = 0.3x + 12.25$, where x is the number of units produced per hour.

Question 15

Determine whether the lines are parallel, perpendicular, or neither.  
L1: y = $\frac { 9 } { 2 }$ x - 9
L2: y = - $\frac { 2 } { 9 }$ x - 2
 
A)Perpendicular
B)Neither
C)Parallel

Accepted Answer

The slopes of L1 and L2 are $\frac{9}{2}$ and $-\frac{2}{9}$, respectively. Since the product of the slopes is -1 ($\frac{9}{2} * -\frac{2}{9} = -1$), the lines are perpendicular.

Question 16

The graph shows the average salaries for senior high school principals from 1996 through 2008. ​  ​
Find the slope of the line segment connecting the points for the years 1998 and 2002.
​
A)-2394
B)2391
C)-2391
D)2396
E)2392

Accepted Answer

The answer of The graph shows the average salaries for...

Question 17

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. ​  Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.
​
A)-5.07
B)2.07
C)7.07
D)3.07
E)-2.07

Accepted Answer

To find the slope of the line segment connecting the points for the years 2003 and 2004, we need to calculate the change in sales over that time period (which is the rise over run or delta y over delta x).

Sales in 2003 = $6 billion
Sales in 2004 = $8 billion

So the change in sales = $8 billion - $6 billion = $2 billion

The time period is 1 year, so delta x = 1.

Therefore, the slope = delta y / delta x = $2 billion / 1 year = $2 billion/year.

Rounded to two decimal places, this is 2.07 billion/year.

So the best choice is B) 2.07.

Question 18

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is   $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ .
 
X-intercept: (3, 0)
Y-intercept: (0, 9)
 
A) $3 x + 9 y - 27 = 0$
B) $9 x + 3 y - 27 = 0$
C) $3 x + 9 y + 27 = 0$
D) $9 x + 3 y + 27 = 0$
E) $9 x - 3 y - 27 = 0$

Accepted Answer

The answer of Use the intercept form to find the...

Question 19

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.  
A) $L = 0.3 S$
B) $L = 0.7 S$
C) $S = 0.7 L$
D) $S = 70 L$
E) $S = 0.3 L$

Accepted Answer

A 70% discount means the customer pays 30% of the list price, so the sale price $S$ is 30% ($0.3$) of the list price $L$, which is represented by $S = 0.3 L$.

Question 20

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.  
A) $W = - 0.02 S + 2600$
B) $W = - 0.02 S - 2600$
C) $W = 0.02 S + 2600$
D) $S = 0.02 W - 2600$
E) $S = 0.02 W + 2600$

Accepted Answer

The correct equation is $W = 0.02 S + 2600$, as it represents a base salary of $2600 plus 2% of the sales amount S.

Quiz 1: Functions and Their Graphs

A sales representative of a company using a personal car receives $160 per day for lodging and meals plus $0.53 per mile driven.Select a linear equation giving the daily cost C to the company in terms of x, the number of miles driven.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ X-intercept: (-3, 0) Y-intercept: (0, 8)

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ X-intercept: ( $- \frac { 5 } { 8 }$ , 0) Y-intercept: $( 0 , - 3 )$

A school district purchases a high-volume printer, copier, and scanner for $20,000. After 10 years, the equipment will have to be replaced.Its value at that time is expected to be $2,600.Select a linear equation giving the value of the equipment during the 10 years it will be in use.

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = 134.

A sub shop purchases a used pizza oven for $885.After 5 years, the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use.

Estimate the slope of the line.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 1 } { 2 }$ x - 4 L2: y = - $\frac { 1 } { 2 }$ x - 2

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = -20.

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $\frac { 5 } { 100 }$ .Approximate the amount of vertical change in your position if you drive 400 feet.

A microchip manufacturer pays its assembly line workers $12.25 per hour.In addition, workers receive a piecework rate of $0.3 per unit produced.Select a linear equation for the hourly wage W in terms of the number of units x produced per hour.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 9 } { 2 }$ x - 9 L2: y = - $\frac { 2 } { 9 }$ x - 2

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ . X-intercept: (3, 0) Y-intercept: (0, 9)

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.

Quiz 1: Functions and Their Graphs

A sales representative of a company using a personal car receives $160 per day for lodging and meals plus $0.53 per mile driven.Select a linear equation giving the daily cost C to the company in terms of x, the number of miles driven.

A school district purchases a high-volume printer, copier, and scanner for $20,000. After 10 years, the equipment will have to be replaced.Its value at that time is expected to be $2,600.Select a linear equation giving the value of the equipment during the 10 years it will be in use.

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​ The line has a slope of m = 134. ​

A sub shop purchases a used pizza oven for $885.After 5 years, the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use.

Estimate the slope of the line. ​ ​

Determine whether the lines are parallel, perpendicular, or neither. L1: y = 12\frac { 1 } { 2 }21​ x - 4 L2: y = - 12\frac { 1 } { 2 }21​ x - 2

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​ The line has a slope of m = -20. ​

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​ The line has a slope of m = 500. ​

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is 5100\frac { 5 } { 100 }1005​ .Approximate the amount of vertical change in your position if you drive 400 feet.

A microchip manufacturer pays its assembly line workers $12.25 per hour.In addition, workers receive a piecework rate of $0.3 per unit produced.Select a linear equation for the hourly wage W in terms of the number of units x produced per hour.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = 92\frac { 9 } { 2 }29​ x - 9 L2: y = - 29\frac { 2 } { 9 }92​ x - 2

The graph shows the average salaries for senior high school principals from 1996 through 2008. ​ ​ Find the slope of the line segment connecting the points for the years 1998 and 2002. ​

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. ​ Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places. ​

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S.

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = 134.

Estimate the slope of the line.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 1 } { 2 }$ x - 4 L2: y = - $\frac { 1 } { 2 }$ x - 2

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = -20.

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $\frac { 5 } { 100 }$ .Approximate the amount of vertical change in your position if you drive 400 feet.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 9 } { 2 }$ x - 9 L2: y = - $\frac { 2 } { 9 }$ x - 2

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.