Question 1

Solve the problem.
-The change in a certain engineer's salary over time can be approximated by the linear equation y = 1500x + 47,500 where y represents salary in dollars and x represents number of years on the job.According to this equation, after how many years on the job was the engineer's salary $64,000?
A)13 years
B)11 years
C)12 years
D)10 years

Accepted Answer

To find the number of years (x) when the engineer's salary (y) was $64,000, substitute $64,000 for y in the equation and solve for x: $64,000 = 1500x + 47,500. Subtracting 47,500 from both sides gives $16,500 = 1500x. Dividing both sides by 1500 gives x = 11.

Question 2

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (2,0) $ and $ (-8,-3) $
A) $ y=-\frac{3}{10} x-\frac{3}{5} $
B) $ y=\frac{2}{5} x-\frac{31}{5} $
C) $ y=-\frac{2}{5} x-\frac{31}{5} $
D) $ y=\frac{3}{10} x-\frac{3}{5} $

Accepted Answer

The answer of Find an equation in slope-intercept form (where...

Question 3

Find the slope of the line.
-$$
2 x+4 y=0
$$
A) 2
B) 0
C) $ \frac{1}{2} $
D) $ -\frac{1}{2} $

Accepted Answer

To find the slope of the line given by the equation $2x + 4y = 0$, we can rearrange it into slope-intercept form, $y = mx + b$, where $m$ is the slope. Solving for $y$, we get $y = -\frac{1}{2}x$. Therefore, the slope $m = -\frac{1}{2}$.

Question 4

Find an equation in slope-intercept form (where possible) for the line.
-$ y $-intercept $ -1, x $-intercept 2
A) $ y=-2 x+2 $
B) $ y=2 x+2 $
C) $ y=\frac{1}{2} x-1 $
D) $ y=-\frac{1}{2} x-1 $

Accepted Answer

The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope $m$ can be found using the points (2,0) and (0,-1), giving $m = \frac{-1-0}{0-2} = \frac{1}{2}$. Thus, with $b = -1$, the equation is $y = \frac{1}{2}x - 1$.

Question 5

Solve the problem.
-Midtown Delivery Service delivers packages which cost $1.10 per package to deliver. The fixed cost to run the delivery truck is $60 per day. If the company charges $7.10 per package, how many Packages must be delivered daily to break even?
A)54 packages
B)7 packages
C)10 packages
D)6 packages

Accepted Answer

The answer of Solve the problem.
-Midtown Delivery Service delivers packages...

Question 6

Find the equation of the least squares line.
-Two different tests are designed to measure employee productivity and dexterity. Several employees of a company are randomly selected and asked to complete the tests. The results are Below.

A) $ y=75.3-0.329 x $
B) $ y=10.7+1.53 x $
C) $ y=5.05+1.91 x $
D) $ y=2.36+2.03 x $

Accepted Answer

The answer of Find the equation of the least squares...

Question 7

Solve the problem.
-The cost of owning a home includes both fixed costs and variable utility costs. Assume that it costs $5682 per month for mortgage and insurance payments and it costs an average of $1.35 per unit for Natural gas, electricity, and water usage. Determine a linear equation that computes the annual cost Of owning this home if x utility units are used.
A)y = -1.35x + 68,184
B)y = 1.35x + 5682
C)y = -1.35x + 5682
D)y = 1.35x + 68,184

Accepted Answer

The annual cost of owning the home includes the fixed monthly costs ($5682) and the variable costs for utilities ($1.35 per unit). The fixed costs are $5682 per month, so annually this is $5682 * 12 = $68,184. The variable cost is $1.35 per unit of utility used, so the total annual cost is $68,184 (fixed) + $1.35x (variable), where x is the number of utility units used. Therefore, the correct equation is y = 1.35x + 68,184.

Question 8

Evaluate the function as indicated.
-Find f(5.2)when f(x)= 7
A)5.2
B)36.4
C)7
D)-7

Accepted Answer

The function f(x) = 7 means that for any value of x, the output is always 7. Therefore, f(5.2) = 7.

Question 9

Evaluate the function as indicated.
-Find $ f(0) $ when $ f(x)=14 x+13 $.
A) 0
B) 14
C) 13
D) 27

Accepted Answer

To find $ f(0) $, substitute $ x = 0 $ into the function $ f(x) = 14x + 13 $, which gives $ f(0) = 14(0) + 13 = 13 $.

Question 10

Solve the problem.
-Find the temperature at which the Celsius and Fahrenheit scales coincide.
A)-25°
B)0°
C)-40°
D)39°

Accepted Answer

The formula to convert Celsius to Fahrenheit is $F = \frac{9}{5}C + 32$. To find where they coincide, set $F = C$ and solve: $C = \frac{9}{5}C + 32$. Simplifying, $C = -40$.

Question 11

Graph the equation.
-5x + y = -4   
A) 
B)

Accepted Answer

The answer of Graph the equation.
-5x + y = -4...

Question 12

Find the slope of the line.
-A line perpendicular to $ 9 x+4 y=50 $
A) $ \frac{9}{4} $
B) $ -\frac{4}{9} $
C) $ \frac{4}{9} $
D) 9

Accepted Answer

The slope of the line $9x + 4y = 50$ is $-\frac{9}{4}$. A line perpendicular to this will have a slope that is the negative reciprocal, which is $\frac{4}{9}$.

Question 13

Find the slope of the line passing through the given pair of points.
-$ (-9,-4) $ and $ (-9,-9) $
A) $ -\frac{5}{18} $
B) Not defined
C) $ \frac{13}{18} $
D) 0

Accepted Answer

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$. Here, since $x_1 = x_2 = -9$, the denominator becomes 0, which means the slope is undefined. This corresponds to a vertical line.

Question 14

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (0,3), \mathrm{m}=\frac{2}{3} $
A) $ y=\frac{2}{3} x+3 $
B) $ y=-\frac{2}{3} x+3 $
C) $ y=\frac{2}{3} x-3 $
D) $ y=-\frac{2}{3} x-3 $

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given the slope $m = \frac{2}{3}$ and the y-intercept $b = 3$ (since the line passes through $0,3$), the equation is $y = \frac{2}{3}x + 3$.

Question 15

Write a cost function for the problem. Assume that the relationship is linear.
-A moving firm charges a flat fee of $40 plus $35 per hour. Let C(x)be the cost in dollars of using the moving firm for x hours.
A)C(x)= 40x + 35
B)C(x)= 35x + 40
C)C(x)= 35x - 40
D)C(x)= 40x - 35

Accepted Answer

The correct cost function is C(x) = 35x + 40, where 35 represents the cost per hour and 40 is the flat fee.

Question 16

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (5,0), m=-1 $
A) $ y=-x+5 $
B) $ y=x-5 $
C) $ y=-5 x $
D) $ y=5 x $

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given a point $(5,0)$ and a slope $m = -1$, we substitute these values into the slope-intercept form to find $b$. Substituting $m = -1$ and the point $(5,0)$ gives $0 = -1(5) + b$, solving for $b$ gives $b = 5$. Thus, the equation is $y = -x + 5$.

Question 17

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (4,10) $, parallel to $ -4 x+3 y=-13 $
A) $ y=\frac{3}{4} x-\frac{5}{2} $
B) $ y=-\frac{4}{3} x-\frac{14}{3} $
C) $ y=-\frac{4}{3} x-\frac{13}{3} $
D) $ y=\frac{4}{3} x+\frac{14}{3} $

Accepted Answer

The answer of Find an equation in slope-intercept form (where...

Question 18

Solve the problem.
-A car rental company charges $33 per day to rent a particular type of car and $0.15 per mile. Juan is charged $56.70 for a one-day rental. How many miles did he drive?
A)173 mi
B)158 mi
C)345 mi
D)378 mi

Accepted Answer

To find the number of miles Juan drove, we first subtract the daily rental charge from the total charge: $56.70 - $33 = $23.70. Then, we divide the remaining amount by the per-mile charge: $23.70 / $0.15 = 158 miles.

Question 19

Solve the problem.
-For the following table of data, 
a. Draw a scatterplot.
B. Calculate the correlation coefficient.
C. Calculate the least squares line and graph it on the scatterplot.
D. Predict the y-value when x is 11.

A) 
B) 
C)

D)

Accepted Answer

The answer of Solve the problem.
-For the following table of...

Question 20

Solve the problem.
-The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands). Use the equation of the least squares line to predict the number of Products sold if the cost of advertising is $6000. 
A)72.54 products sold
B)69.54 products sold
C)16,795.8 products sold
D)79.24 products sold

Accepted Answer

The answer of Solve the problem.
-The paired data below consist...

Quiz 1: Linear Functions

Find an equation in slope-intercept form (where possible) for the line. -Through $(2,0)$ and $(-8,-3)$

Find the slope of the line. - $2 x+4 y=0$

Find an equation in slope-intercept form (where possible) for the line. - $y$ -intercept $-1, x$ -intercept 2

Solve the problem. -Midtown Delivery Service delivers packages which cost $1.10 per package to deliver. The fixed cost to run the delivery truck is $60 per day. If the company charges $7.10 per package, how many Packages must be delivered daily to break even?

Find the equation of the least squares line. -Two different tests are designed to measure employee productivity and dexterity. Several employees of a company are randomly selected and asked to complete the tests. The results are Below.

Evaluate the function as indicated. -Find f(5.2) when f(x) = 7

Evaluate the function as indicated. -Find $f(0)$ when $f(x) =14 x+13$ .

Solve the problem. -Find the temperature at which the Celsius and Fahrenheit scales coincide.

Graph the equation. -5x + y = -4

Find the slope of the line. -A line perpendicular to $9 x+4 y=50$

Find the slope of the line passing through the given pair of points. - $(-9,-4)$ and $(-9,-9)$

Find an equation in slope-intercept form (where possible) for the line. -Through $(0,3) , \mathrm{m}=\frac{2}{3}$

Write a cost function for the problem. Assume that the relationship is linear. -A moving firm charges a flat fee of $40 plus $35 per hour. Let C(x) be the cost in dollars of using the moving firm for x hours.

Find an equation in slope-intercept form (where possible) for the line. -Through $(5,0) , m=-1$

Find an equation in slope-intercept form (where possible) for the line. -Through $(4,10)$ , parallel to $-4 x+3 y=-13$

Solve the problem. -A car rental company charges $33 per day to rent a particular type of car and $0.15 per mile. Juan is charged $56.70 for a one-day rental. How many miles did he drive?

Solve the problem. -For the following table of data, a. Draw a scatterplot. B. Calculate the correlation coefficient. C. Calculate the least squares line and graph it on the scatterplot. D. Predict the y-value when x is 11.

Solve the problem. -The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands) . Use the equation of the least squares line to predict the number of Products sold if the cost of advertising is $6000.

Quiz 1: Linear Functions

Find an equation in slope-intercept form (where possible) for the line. -Through (2,0) (2,0) (2,0) and (−8,−3) (-8,-3) (−8,−3)

Find the slope of the line. - 2x+4y=02 x+4 y=02x+4y=0

Find an equation in slope-intercept form (where possible) for the line. - y y y -intercept −1,x -1, x −1,x -intercept 2