Question 1

Write the equation in slope-intercept form.
-$-x+2 y=5$

Accepted Answer

A)  $y=\frac{1}{2} x+\frac{5}{2}$ 
B)  $y=x-\frac{5}{2}$ 
C)  $y=-\frac{1}{2} x+\frac{5}{2}$ 
D)  $y=\frac{1}{2} x-5$ 
A)  $y=\frac{1}{2} x+\frac{5}{2}$ 
B)  $y=x-\frac{5}{2}$ 
C)  $y=-\frac{1}{2} x+\frac{5}{2}$ 
D)  $y=\frac{1}{2} x-5$

Question 2

Determine whether the relation defines $y$ as a function of $x$. Give the domain.
-$y=-\frac{4}{x}$

Accepted Answer

A)  Function; domain $(-\infty, 0) \cup(0, \infty)$ 
B)  Not a function; domain $(-\infty, 4) \cup(4, \infty)$ 
C)  Not a function; domain $(-\infty, 0) \cup(0, \infty)$ 
D)  Function; domain: $(-\infty, \infty)$ 
A)  Function; domain $(-\infty, 0) \cup(0, \infty)$ 
B)  Not a function; domain $(-\infty, 4) \cup(4, \infty)$ 
C)  Not a function; domain $(-\infty, 0) \cup(0, \infty)$ 
D)  Function; domain: $(-\infty, \infty)$

Question 3

Determine whether the relation defines $y$ as a function of $x$. Give the domain.
-$y=\frac{-9}{x+11}$

Accepted Answer

A)  Not a function; domain: $(-\infty,-11) \cup(-11,0)$ 
B)  Function; domain: $(-\infty,-11) \cup(-11, \infty)$ 
C)  Function; domain: $(-11,11)$ 
D)  Not a function; domain: $(-\infty, \infty)$ 
A)  Not a function; domain: $(-\infty,-11) \cup(-11,0)$ 
B)  Function; domain: $(-\infty,-11) \cup(-11, \infty)$ 
C)  Function; domain: $(-11,11)$ 
D)  Not a function; domain: $(-\infty, \infty)$

Question 4

Find the slope of the line and sketch the graph.
-$2 x+3 y=10$

Accepted Answer

A)  Slope: $\frac{3}{2}$
  
B)  Slope: $-\frac{3}{2}$
  
C)  Slope: $-\frac{2}{3}$
  
D)  Slope: $\frac{2}{3}$
  
A)  Slope: $\frac{3}{2}$
  
B)  Slope: $-\frac{3}{2}$
  
C)  Slope: $-\frac{2}{3}$
  
D)  Slope: $\frac{2}{3}$

Question 5

Solve the problem.
-The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

Accepted Answer

A)  $y-4 x=-5$ 
B)  $y=-4 x+3$ 
C)  $y-4 x=3$ 
D)  $y+4 x=-5$ 
A)  $y-4 x=-5$ 
B)  $y=-4 x+3$ 
C)  $y-4 x=3$ 
D)  $y+4 x=-5$

Question 6

Give the domain and range of the relation shown in the following.
-

Accepted Answer

A)  Domain: $(-\infty,-3]$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty,-3]$ 
C)  Domain: $[-3, \infty)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-3, \infty)$; range: $(-\infty, \infty)$ 
A)  Domain: $(-\infty,-3]$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty,-3]$ 
C)  Domain: $[-3, \infty)$; range: $(-\infty, \infty)$ 
D)  Domain: $(-3, \infty)$; range: $(-\infty, \infty)$

Question 7

The boundary of the graph of the linear inequality will be a _____ line, and the shading will be _____ the line. Fill in the first blank with either solid or dashed. Fill in the second blank with above or below.
-$y \leq 3 x-\frac{3}{2}$

Accepted Answer

A)  dashed; above 
B)  solid; above 
C)  dashed; below 
D)  solid; below 
A)  dashed; above 
B)  solid; above 
C)  dashed; below 
D)  solid; below

Question 8

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q$.
-$P(5,5)$ and $M\biggl(\frac{9}{2}, \frac{9}{2}\biggl)$

Accepted Answer

A)  $Q(9,9)$ 
B)  $\mathrm{Q}\biggl(\frac{1}{2}, \frac{1}{2}\biggl)$ 
C)  $\mathrm{Q}(4,4)$ 
D)  $Q(1,1)$ 
A)  $Q(9,9)$ 
B)  $\mathrm{Q}\biggl(\frac{1}{2}, \frac{1}{2}\biggl)$ 
C)  $\mathrm{Q}(4,4)$ 
D)  $Q(1,1)$

Question 9

Solve the problem.
-The function $\mathrm{H}$ described by $\mathrm{H}(\mathrm{x})=2.75 \mathrm{x}+71.48$ can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is $x \mathrm{~cm}$ long. Estimate the height of a woman whose humerus is $31.1 \mathrm{~cm}$ long.

Accepted Answer

A)  $105.33 \mathrm{~cm}$ 
B)  $43.13 \mathrm{~cm}$ 
C)  $157.005 \mathrm{~cm}$ 
D)  $14.045 \mathrm{~cm}$ 
A)  $105.33 \mathrm{~cm}$ 
B)  $43.13 \mathrm{~cm}$ 
C)  $157.005 \mathrm{~cm}$ 
D)  $14.045 \mathrm{~cm}$

Question 10

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
-$(4,7)$ and $(7,7)$

Accepted Answer

A)  -3 ; falls 
B)  3; rises 
C)  0; horizontal 
D)  Undefined; vertical 
A)  -3 ; falls 
B)  3; rises 
C)  0; horizontal 
D)  Undefined; vertical

Question 11

Find the midpoint of the segment with the given endpoints.
-$(2,-2)$ and $(7,-6)$

Accepted Answer

A)  $(-5,4)$ 
B)  $(9,-8)$ 
C)  $\biggl(\frac{9}{2},-4\biggl)$ 
D)  $\biggl(-\frac{5}{2}, 2\biggl)$ 
A)  $(-5,4)$ 
B)  $(9,-8)$ 
C)  $\biggl(\frac{9}{2},-4\biggl)$ 
D)  $\biggl(-\frac{5}{2}, 2\biggl)$

Question 12

Write the equation in slope-intercept form.
-$x-8 y=8$

Accepted Answer

A)  $y=\frac{1}{8} x-8$ 
B)  $y=\frac{1}{8} x-1$ 
C)  $y=8 x-8$ 
D)  $y=x-1$ 
A)  $y=\frac{1}{8} x-8$ 
B)  $y=\frac{1}{8} x-1$ 
C)  $y=8 x-8$ 
D)  $y=x-1$

Question 13

Choose the inequality that best matches the given calculator graph.
-

Accepted Answer

A)  $y \geq 2 x-2$ 
B)  $y \leq-2 x+2$ 
C)  $y \leq 2 x-2$ 
D)  $y \geq-2 x-2$ 
A)  $y \geq 2 x-2$ 
B)  $y \leq-2 x+2$ 
C)  $y \leq 2 x-2$ 
D)  $y \geq-2 x-2$

Question 14

Find the slope of the line and sketch the graph.
-$y-2=0$

Accepted Answer

A)  Slope: 0
  
B)  Slope: 2
  
C)  Slope: $\frac{1}{2}$
  
D)  Slope: Undefined
  
A)  Slope: 0
  
B)  Slope: 2
  
C)  Slope: $\frac{1}{2}$
  
D)  Slope: Undefined

Question 15

Decide whether the relation is a function.
-$\{(-5,-8),(-2,8),(2,1),(5,-4)\}$

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 16

Determine the quadrants in which the given point $(x, y)$ may lie when $x>0$.

Accepted Answer

A)  II or IV 
B)  I or III 
C)  I or IV 
D)  I or II 
A)  II or IV 
B)  I or III 
C)  I or IV 
D)  I or II

Question 17

Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
-Through $(-6,7)$; parallel to $3 x+7 y=3$

Accepted Answer

A)  $y=\frac{3}{7} x+\frac{3}{7}$ 
B)  $y=-\frac{7}{3} x+\frac{7}{3}$ 
C)  $y=-\frac{3}{7} x+\frac{31}{7}$ 
D)  $y=\frac{3}{7} x-\frac{31}{7}$ 
A)  $y=\frac{3}{7} x+\frac{3}{7}$ 
B)  $y=-\frac{7}{3} x+\frac{7}{3}$ 
C)  $y=-\frac{3}{7} x+\frac{31}{7}$ 
D)  $y=\frac{3}{7} x-\frac{31}{7}$

Question 18

Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
-Through $(-3,8)$; perpendicular to $-3 x+4 y=-23$

Accepted Answer

A)  $y=\frac{3}{4} x+\frac{41}{4}$ 
B)  $y=\frac{4}{3} x+12$ 
C)  $y=-\frac{4}{3} x+4$ 
D)  $y=-\frac{3}{4} x+\frac{23}{4}$ 
A)  $y=\frac{3}{4} x+\frac{41}{4}$ 
B)  $y=\frac{4}{3} x+12$ 
C)  $y=-\frac{4}{3} x+4$ 
D)  $y=-\frac{3}{4} x+\frac{23}{4}$

Question 19

Find the slope and the $y$-intercept of the line.
-$7 x+5 y=48$

Accepted Answer

A)  Slope $\frac{5}{7} ; y$-intercept $\biggl(0, \frac{5}{48}\biggl)$ 
B)  Slope $-\frac{7}{5} ; y$-intercept $\biggl(0, \frac{48}{5}\biggl)$ 
C)  Slope $\frac{7}{5} ; y$-intercept $\biggl(0, \frac{48}{5}\biggl)$ 
D)  Slope $-\frac{5}{7} ; \mathrm{y}$-intercept $\biggl(0, \frac{5}{48}\biggl)$ 
A)  Slope $\frac{5}{7} ; y$-intercept $\biggl(0, \frac{5}{48}\biggl)$ 
B)  Slope $-\frac{7}{5} ; y$-intercept $\biggl(0, \frac{48}{5}\biggl)$ 
C)  Slope $\frac{7}{5} ; y$-intercept $\biggl(0, \frac{48}{5}\biggl)$ 
D)  Slope $-\frac{5}{7} ; \mathrm{y}$-intercept $\biggl(0, \frac{5}{48}\biggl)$

Question 20

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.
  
-$(-5,-4)$

Accepted Answer

A)  I 
B)  A 
C)  $\mathrm{L}$ 
D)  $G$ 
A)  I 
B)  A 
C)  $\mathrm{L}$ 
D)  $G$

Write the equation in slope-intercept form. - $-x+2 y=5$

Determine whether the relation defines $y$ as a function of $x$ . Give the domain. - $y=-\frac{4}{x}$

Determine whether the relation defines $y$ as a function of $x$ . Give the domain. - $y=\frac{-9}{x+11}$

Find the slope of the line and sketch the graph. - $2 x+3 y=10$

Solve the problem. -The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

Give the domain and range of the relation shown in the following. -

The boundary of the graph of the linear inequality will be a _ line, and the shading will be _ the line. Fill in the first blank with either solid or dashed. Fill in the second blank with above or below. - $y \leq 3 x-\frac{3}{2}$

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ . - $P(5,5)$ and $M\biggl(\frac{9}{2}, \frac{9}{2}\biggl)$

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. - $(4,7)$ and $(7,7)$

Find the midpoint of the segment with the given endpoints. - $(2,-2)$ and $(7,-6)$

Write the equation in slope-intercept form. - $x-8 y=8$

Choose the inequality that best matches the given calculator graph. -

Find the slope of the line and sketch the graph. - $y-2=0$

Decide whether the relation is a function. - $\{(-5,-8),(-2,8),(2,1),(5,-4)\}$

Determine the quadrants in which the given point $(x, y)$ may lie when $x>0$ .

Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form. -Through $(-6,7)$ ; parallel to $3 x+7 y=3$

Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form. -Through $(-3,8)$ ; perpendicular to $-3 x+4 y=-23$

Find the slope and the $y$ -intercept of the line. - $7 x+5 y=48$

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer. - $(-5,-4)$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 3: Linear Equations, Graphs, and Functions

Write the equation in slope-intercept form. - −x+2y=5-x+2 y=5−x+2y=5

Determine whether the relation defines yyy as a function of xxx . Give the domain. - y=−4xy=-\frac{4}{x}y=−x4​

Determine whether the relation defines yyy as a function of xxx . Give the domain. - y=−9x+11y=\frac{-9}{x+11}y=x+11−9​

Find the slope of the line and sketch the graph. - 2x+3y=102 x+3 y=102x+3y=10