Question 1

Use the formula for slope to find the value of y such that the line through the points (-2,2) and (1,y) has slope of m=$- \frac { 8 } { 3 }$ .

Accepted Answer

A)  y=-2 
B)  y=2 
C)  y=6 
D)  y=5 
E)  $y = - 6$ 
A)  y=-2 
B)  y=2 
C)  y=6 
D)  y=5 
E)  $y = - 6$ E

Question 2

Sketch the graph of the linear inequality $2 ( y - 1 ) \leq x + 2$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 3

Plot the points on a rectangular coordinate system. $( 2,4 ) , ( - 2 , - 4 )$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    B

Question 4

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. Find $T ( 22 )$ .

Accepted Answer

A)  $T ( 22 ) = 66$ 
B)  $T ( 22 ) = 60$ 
C)  $T ( 22 ) = 72$ 
D)  $T ( 22 ) = 22$ 
E)  $T ( 22 ) = 54$ 
A)  $T ( 22 ) = 66$ 
B)  $T ( 22 ) = 60$ 
C)  $T ( 22 ) = 72$ 
D)  $T ( 22 ) = 22$ 
E)  $T ( 22 ) = 54$

Question 5

The table shows the projected number N (in millions)of persons with pets in a certain country. $$\begin{array} { | c | c | c | c | c | } 
\hline \text { Year } & 2010 & 2015 & 2020 & 2025 \
\hline N & 39.15 & 47.8 & 56.81 & 65.96 \
\hline
\end{array}$$ A model for this data is $N = 1.83 t + 20.9$ where t represents time in years, with $t = 10$ corresponding to the year 2010. According to the model, in what year will the number of pet owners exceed $72.14$ million?

Accepted Answer

A)  $2034$ 
B)  $2029$ 
C)  $2024$ 
D)  $2027$ 
E)  $2028$ 
A)  $2034$ 
B)  $2029$ 
C)  $2024$ 
D)  $2027$ 
E)  $2028$

Question 6

Write the equation of the line that passes through the point (2,-2) and has slope m=-4 . Write the equation in slope-intercept form.

Accepted Answer

A)  y=4x 
B)   y=-4x-2 
C)  y=4x+2 
D)  y=-4x+6 
E)  y=-4x-6 
A)  y=4x 
B)   y=-4x-2 
C)  y=4x+2 
D)  y=-4x+6 
E)  y=-4x-6

Question 7

Write an equation for a line that passes through (8,-8) and is perpendicular to $5 x + 8 y = 26$ .

Accepted Answer

A)  $y = - \frac { 5 } { 8 } x - \frac { 56 } { 5 }$ 
B)  $y = - \frac { 5 } { 8 } x - \frac { 104 } { 5 }$ 
C)  $y = - \frac { 8 } { 5 } x - \frac { 104 } { 5 }$ 
D)  $y = \frac { 5 } { 8 } x + \frac { 104 } { 5 }$ 
E)  $y = \frac { 8 } { 5 } x - \frac { 104 } { 5 }$ 
A)  $y = - \frac { 5 } { 8 } x - \frac { 56 } { 5 }$ 
B)  $y = - \frac { 5 } { 8 } x - \frac { 104 } { 5 }$ 
C)  $y = - \frac { 8 } { 5 } x - \frac { 104 } { 5 }$ 
D)  $y = \frac { 5 } { 8 } x + \frac { 104 } { 5 }$ 
E)  $y = \frac { 8 } { 5 } x - \frac { 104 } { 5 }$

Question 8

Evaluate and simplify $f ( x ) = 12 x - 7$ at $x = \frac { 11 } { 2 }$ .

Accepted Answer

A)  $f \left( \frac { 11 } { 2 } \right) = 139$ 
B)  $f \left( \frac { 11 } { 2 } \right) = 73$ 
C)  $f \left( \frac { 11 } { 2 } \right) = 59$ 
D)  $f \left( \frac { 11 } { 2 } \right) = 66$ 
E)  $f \left( \frac { 11 } { 2 } \right) = 125$ 
A)  $f \left( \frac { 11 } { 2 } \right) = 139$ 
B)  $f \left( \frac { 11 } { 2 } \right) = 73$ 
C)  $f \left( \frac { 11 } { 2 } \right) = 59$ 
D)  $f \left( \frac { 11 } { 2 } \right) = 66$ 
E)  $f \left( \frac { 11 } { 2 } \right) = 125$

Question 9

The point (1,2) is on a line with undefined slope. Find two additional points on the line.

Accepted Answer

A)  (2,1) and (0,3) 
B)  (1,0) and (1,0) 
C)  (2,3) and (0,1) 
D)   (2,1) and $( 0,2 )$ 
E)  $( 1,3 )$ and $( 1,1 )$ 
A)  (2,1) and (0,3) 
B)  (1,0) and (1,0) 
C)  (2,3) and (0,1) 
D)   (2,1) and $( 0,2 )$ 
E)  $( 1,3 )$ and $( 1,1 )$

Question 10

Write an inequality for the shaded region shown.

Accepted Answer

A)  $y \leq - 2 x - 1$ 
B)  $y < - 2 x - 1$ 
C)  $y \leq 2 x + 1$ 
D)  $y \leq - 2 x + 1$ 
E)  $y < 2 x + 1$ 
A)  $y \leq - 2 x - 1$ 
B)  $y < - 2 x - 1$ 
C)  $y \leq 2 x + 1$ 
D)  $y \leq - 2 x + 1$ 
E)  $y < 2 x + 1$

Question 11

Which inequality corresponds to the given graph?

Accepted Answer

A)  $- x + y  0$ 
C)  $- x - y \geq 0$ 
D)  $- x + y \geq 0$ 
E)  $- x + y \leq 0$ 
A)  $- x + y  0$ 
C)  $- x - y \geq 0$ 
D)  $- x + y \geq 0$ 
E)  $- x + y \leq 0$

Question 12

Use the Distance Formula to determine whether the points $( 7,9 ) , ( 7,4 )$ and $( 7,7 )$ are collinear.

Accepted Answer

A)  $\text { not collinear }$ 
B)  $\text { collinear }$ 
A)  $\text { not collinear }$ 
B)  $\text { collinear }$

Question 13

State if the line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises, falls, is horizontal, or is vertical.

Accepted Answer

A) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises. 
B) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ horizontal. 
C) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ falls. 
D) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ vertical. 
A) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises. 
B) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ horizontal. 
C) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ falls. 
D) The line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ vertical.

Question 14

A bicycle that was purchased for $\$ 150$ depreciates to a value of $\$ 128$ after one year. Assuming that depreciation is linear estimate the bicycle s value after 5 years.

Accepted Answer

A) $ $108$ 
B) $ $55$ 
C) $ $125$ 
D) $ $100$ 
E) $ $40$ 
A) $ $108$ 
B) $ $55$ 
C) $ $125$ 
D) $ $100$ 
E) $ $40$

Question 15

Sketch the graph of the linear inequality $3 x - 2 y \leq - 6$.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

A right triangle has vertices at $A ( - 4,3 ) , B ( 3,5 )$ and $C ( 5 , - 2 )$ . Find the length of the three line segments, AB , BC , AC . Round your answer to two decimal places.

Accepted Answer

A)  $A B = 8.06 , B C = 7.28 , A C = 10.30$ 
B)  $A B = 8.06 , B C = 9.43 , A C = 10.30$ 
C)  $A B = 7.28 , B C = 7.28 , A C = 1.41$ 
D)  $A B = 7.28 , B C = 9.43 , A C = 10.30$ 
E)  $A B = 7.28 , B C = 7.28 , A C = 10.30$ 
A)  $A B = 8.06 , B C = 7.28 , A C = 10.30$ 
B)  $A B = 8.06 , B C = 9.43 , A C = 10.30$ 
C)  $A B = 7.28 , B C = 7.28 , A C = 1.41$ 
D)  $A B = 7.28 , B C = 9.43 , A C = 10.30$ 
E)  $A B = 7.28 , B C = 7.28 , A C = 10.30$

Question 17

Write the surface area S of a cube as a function of the length x of one of its edges, and use it to find the surface area (in square inches)when $x = 5$ inches.

Accepted Answer

A)  $S ( 5 ) = 25$ square inches 
B)  $S ( 5 ) = 750$ square inches 
C)  $S ( 5 ) = 30$ square inches 
D)  $S ( 5 ) = 100$ square inches 
E)  $S ( 5 ) = 150$ square inches 
A)  $S ( 5 ) = 25$ square inches 
B)  $S ( 5 ) = 750$ square inches 
C)  $S ( 5 ) = 30$ square inches 
D)  $S ( 5 ) = 100$ square inches 
E)  $S ( 5 ) = 150$ square inches

Question 18

Your company purchases a new delivery van for $\$ 56,000$ . For tax purposes, the van will be depreciated over a seven year period. At the end of seven years, the value of the van is expected to be $7000 . Find a linear equation that relates the depreciated value of the van, y , to the number of years, t , since it was purchased.

Accepted Answer

A)  $y = 56,000 + 7000 t$ 
B)  $y = 7000 - 56,000 t$ 
C)  $y = 56,000 - 49,000 t$ 
D)  $y = 49,000 - 7000 t$ 
E)  $y = 56,000 - 7000 t$ 
A)  $y = 56,000 + 7000 t$ 
B)  $y = 7000 - 56,000 t$ 
C)  $y = 56,000 - 49,000 t$ 
D)  $y = 49,000 - 7000 t$ 
E)  $y = 56,000 - 7000 t$

Question 19

A store is offering a 30% discount on all items in its inventory. Write an equation of the line giving the sales price S for an item in terms of its list price L .

Accepted Answer

A)  $\mathrm { S } = - 0.7 L$ 
B)  $S = - 29 L$ 
C)  $S = 0.7 L$ 
D)  $S = 1.3 L$ 
E)  $S = - 2 L$ 
A)  $\mathrm { S } = - 0.7 L$ 
B)  $S = - 29 L$ 
C)  $S = 0.7 L$ 
D)  $S = 1.3 L$ 
E)  $S = - 2 L$

Question 20

Graph the equation $y = - | x | + 6$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Use the formula for slope to find the value of y such that the line through the points (-2,2) and (1,y) has slope of m= $- \frac { 8 } { 3 }$ .

Sketch the graph of the linear inequality $2 ( y - 1 ) \leq x + 2$ .

Plot the points on a rectangular coordinate system. $( 2,4 ) , ( - 2 , - 4 )$

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. Find $T ( 22 )$ .

Write the equation of the line that passes through the point (2,-2) and has slope m=-4 . Write the equation in slope-intercept form.

Write an equation for a line that passes through (8,-8) and is perpendicular to $5 x + 8 y = 26$ .

Evaluate and simplify $f ( x ) = 12 x - 7$ at $x = \frac { 11 } { 2 }$ .

The point (1,2) is on a line with undefined slope. Find two additional points on the line.

Write an inequality for the shaded region shown.

Which inequality corresponds to the given graph?

Use the Distance Formula to determine whether the points $( 7,9 ) , ( 7,4 )$ and $( 7,7 )$ are collinear.

State if the line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises, falls, is horizontal, or is vertical.

A bicycle that was purchased for $\$ 150$ depreciates to a value of $\$ 128$ after one year. Assuming that depreciation is linear estimate the bicycle s value after 5 years.

Sketch the graph of the linear inequality $3 x - 2 y \leq - 6$ .

A right triangle has vertices at $A ( - 4,3 ) , B ( 3,5 )$ and $C ( 5 , - 2 )$ . Find the length of the three line segments, AB , BC , AC . Round your answer to two decimal places.

Write the surface area S of a cube as a function of the length x of one of its edges, and use it to find the surface area (in square inches)when $x = 5$ inches.

A store is offering a 30% discount on all items in its inventory. Write an equation of the line giving the sales price S for an item in terms of its list price L .

Graph the equation $y = - | x | + 6$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 3: Graphs and Functions

Use the formula for slope to find the value of y such that the line through the points (-2,2) and (1,y) has slope of m= −83- \frac { 8 } { 3 }−38​ .

Sketch the graph of the linear inequality 2(y−1)≤x+22 ( y - 1 ) \leq x + 22(y−1)≤x+2 .

Plot the points on a rectangular coordinate system. (2,4),(−2,−4)( 2,4 ) , ( - 2 , - 4 )(2,4),(−2,−4)

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. Find T(22)T ( 22 )T(22) .

Write the equation of the line that passes through the point (2,-2) and has slope m=-4 . Write the equation in slope-intercept form.

Write an equation for a line that passes through (8,-8) and is perpendicular to 5x+8y=265 x + 8 y = 265x+8y=26 .

Evaluate and simplify f(x)=12x−7f ( x ) = 12 x - 7f(x)=12x−7 at x=112x = \frac { 11 } { 2 }x=211​ .

The point (1,2) is on a line with undefined slope. Find two additional points on the line.

Write an inequality for the shaded region shown.

Which inequality corresponds to the given graph?

Use the Distance Formula to determine whether the points (7,9),(7,4)( 7,9 ) , ( 7,4 )(7,9),(7,4) and (7,7)( 7,7 )(7,7) are collinear.

State if the line passing through the points (34,9)\left( \frac { 3 } { 4 } , 9 \right)(43​,9) and (6,−52)\left( 6 , - \frac { 5 } { 2 } \right)(6,−25​) rises, falls, is horizontal, or is vertical.

A bicycle that was purchased for $150\$ 150$150 depreciates to a value of $128\$ 128$128 after one year. Assuming that depreciation is linear estimate the bicycle s value after 5 years.

Sketch the graph of the linear inequality 3x−2y≤−63 x - 2 y \leq - 63x−2y≤−6 .

A right triangle has vertices at A(−4,3),B(3,5)A ( - 4,3 ) , B ( 3,5 )A(−4,3),B(3,5) and C(5,−2)C ( 5 , - 2 )C(5,−2) . Find the length of the three line segments, AB , BC , AC . Round your answer to two decimal places.

Write the surface area S of a cube as a function of the length x of one of its edges, and use it to find the surface area (in square inches)when x=5x = 5x=5 inches.

A store is offering a 30% discount on all items in its inventory. Write an equation of the line giving the sales price S for an item in terms of its list price L .

Graph the equation y=−∣x∣+6y = - | x | + 6y=−∣x∣+6 .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Use the formula for slope to find the value of y such that the line through the points (-2,2) and (1,y) has slope of m= $- \frac { 8 } { 3 }$ .

Sketch the graph of the linear inequality $2 ( y - 1 ) \leq x + 2$ .

Plot the points on a rectangular coordinate system. $( 2,4 ) , ( - 2 , - 4 )$

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. Find $T ( 22 )$ .

Write an equation for a line that passes through (8,-8) and is perpendicular to $5 x + 8 y = 26$ .

Evaluate and simplify $f ( x ) = 12 x - 7$ at $x = \frac { 11 } { 2 }$ .

Use the Distance Formula to determine whether the points $( 7,9 ) , ( 7,4 )$ and $( 7,7 )$ are collinear.

State if the line passing through the points $\left( \frac { 3 } { 4 } , 9 \right)$ and $\left( 6 , - \frac { 5 } { 2 } \right)$ rises, falls, is horizontal, or is vertical.

A bicycle that was purchased for $\$ 150$ depreciates to a value of $\$ 128$ after one year. Assuming that depreciation is linear estimate the bicycle s value after 5 years.

Sketch the graph of the linear inequality $3 x - 2 y \leq - 6$ .

A right triangle has vertices at $A ( - 4,3 ) , B ( 3,5 )$ and $C ( 5 , - 2 )$ . Find the length of the three line segments, AB , BC , AC . Round your answer to two decimal places.

Write the surface area S of a cube as a function of the length x of one of its edges, and use it to find the surface area (in square inches)when $x = 5$ inches.

Graph the equation $y = - | x | + 6$ .