```Objective 10
2008
TEKS Tech Cards
Which point on the grid satisfies the conditions x ≥ 5
and y < −1?
A
B
C
D
W
X
Y
Z
[TEKS 8.14C : 2004 #48 ] STUDENT EXPECTATION
Select or develop an appropriate problem-solving strategy from a
variety of different types, including drawing a picture, looking for a
pattern, systematic guessing and checking, acting it out, making a table,
working a simpler problem, or working backwards to solve a problem.
Step 1
First, plot the points
TEKS 8.14C
(Objective 10)
• point
• horizontal line
• vertical line
Step 2
Draw a vertical line to
represent x>5
hold right arrow and
scroll to the right until you get to x=5
Only points x
and w are at or
to the right of
the vertical
line
Step 3
Draw a horizontal line to
represent y<-1
hold down arrow and
scroll down until you get to y=-1
Point x is not
below the line
y= -1 but point w
is. Thus, letter A
Objective 2
2008
TEKS Tech Cards
Sue wants to write an expression that will always
produce an even integer.
Which of the following will always produce an even
integer for any given integer, n?
A
B
C
D
2n + 1
2n – 1
n+2
2n
[TEKS A.3B : 2004 #43] STUDENT EXPECTATION
The student looks for patterns and represents generalizations
algebraically.
Input the first expression
TEKS A. 3B
using x instead of n.
(Objective 2)
Look at the
table of values.
display a screen like the
• expression
one below.
Step 1
• integer
• even integer
• table of values
2n +1
Did your expression produce even integers? NO
Step 2
Repeat the process for the
rest of the expressions. You may input all
expressions at the same time as shown below
Step 3
Look and compare the
tables of values.
The last expression, Y4, is the only one that
produces even integers for any given integer
x. Therefore, letter D is the correct answer.
Objective 2
2008
TEKS Tech Cards
Which is the best representation of the function y = x?
[TEKS A.2A : 2003 #7 ] STUDENT EXPECTATION
The student identifies [and sketches] the general forms of linear, y=x,
and quadratic, y=x², parent functions.
Step 1
Begin by graphing the
given equation, y=x.
TEKS A.2A
(Objective 2)
• function
• parent function
• equation
It is easy to see that letter B, the linear
parent function, is the correct answer.
Step 2
Guide students to come up
with examples for the rest of the answer
choices. Some examples are shown below:
A) y = 5
Step 3
C) y =|x|
D) y = 0.5x²
Objective 3
2008
TEKS Tech Cards
Which equation describes a line that has a
y-intercept of 5 and a slope of ½ ?
F
y=5 + ½ x
G y=(5+x) ½
H y=5x + ½
J
y=(5x + 1) ½
[TEKS A.6D : 2004 #10 ] STUDENT EXPECTATION
The student graphs and writes equations of lines given characteristics
such as two points, a point and a slope, or a slope and y–intercept.
Step 1
Input the first answer
choice into the calculator
TEKS A.6D
(Objective 3)
• equation
Notice how the first
• line
• y-intercept
includes the ordered
• slope
pair (0, 5) on the table of values. Therefore,
• ordered pair
the y-intercept of that line is 5.
Step 2
Similarly, answer choices G,
H, and J do not include the point (0, 5) as
shown below. Thus, the y-intercept for
those lines cannot be 5 and those three
answers can be eliminated.
Step 3
Delete the three wrong
and find the
slope for the first line to ensure the
The slope is
dy/dx = .5 = 1/2
Objective 3
2008
TEKS Tech Cards
The graph of a line that
contains the points (–1, −5)
and (4, 5) is shown to the right.
Which best represents this line
if the slope is doubled and the
y-intercept remains constant?
[TEKS A.6C : 2003 #18 ] STUDENT EXPECTATION
The student investigates, describes, and predicts the effects of changes
in m and b on the graph of y=mx+b
Step 1
Plot the given points
(-1, -5) and (4, 5) using the
function
TEKS A.6C
(Objective 3)
• line
• doubled
• point
• constant
• slope
• steeper
• y-intercept
Step 2
Find the slope and
y-intercept of the equation of the line that
passes through those two points:
So,
b=-3
m=2
Step 3
Double the original slope
(2x2=4) and let the y-intercept (0, -3) remain
the same. Then, graph the new line: y=4x-3.
The new line is
steeper and has the
same y-intercept as
the original one.
Thus, the correct
Objective 3
2008
TEKS Tech Cards
What is the slope of the linear function shown in the
graph?
[TEKS A.6A : 2004 #19 ] STUDENT EXPECTATION
The student develops the concept of slope as rate of change and
determines slopes from graphs, tables, and algebraic representations.
Step 1
Write linear equations in
slope intercept form for all answer choices
using the y-intercept (0, 14) and adjust the
window to match the one on the graph.
A) -7/4 x + 14
B) -4/7 x +14
C) 4/7 x + 14
D) 7/4 x +14
Step 2
A)
• slope
• linear function
• equation
• slope-intercept form
• y-intercept
Graph all equations
Similarly,
B)
Step 3
C)
TEKS A.6A
(Objective 3)
D)
Notice how only the graph from answer
choice B matches with the given one.
Therefore, the correct answer is B.
Objective 3
2008
TEKS Tech Cards
The graph of a linear function is shown on the
coordinate grid below.
If the y-intercept is changed
to (0, 5) and the slope
becomes −4, which
statement best describes
the relationship between
the two lines when they are
graphed on the same
coordinate grid?
A The y-intercepts are 1 unit apart, and the lines are
parallel.
B The y-intercepts are 1 unit apart, and the lines
intersect at (1, 1).
C The y-intercepts are 1 unit apart, and the lines are
perpendicular.
D The y-intercepts are 1 unit apart, and the lines
intersect at (1, 0).
[TEKS A.6C : 2006 #12 ] STUDENT EXPECTATION
The student investigates, describes, and predicts the effects of changes
in m and b on the graph of y=mx+b
Step 1
First, find the equation
of the given line using two points.
TEKS A.6C
(Objective 3)
•linear function • parallel
•coordinate grid • intersect
y = - 5 x + 6 •y-intercept
•slope
•relationship
If the slope changes from
-5 to -4 and the y-intercept
from (0, 6) to (0, 5), the new equation will
be y= -4x + 5. Graph both equations.
Step 2
Step 3
The lines are not parallel
nor perpendicular. Therefore, A and C
cannot be the correct answers. So, we
need to find where the lines intersect.
Since the lines
intersect at (1, 1),
is B
Objective 3
2008
TEKS Tech Cards
The table below shows various values for x and y.
Which equation best describes the relationship
between x and y?
F
G
H
J
y = −3x + 5
y = −5x – 7
y = −x + 17
y = 3x + 41
[TEKS A.5C : 2006 #15 ] STUDENT EXPECTATION
The student translates among and uses algebraic, tabular, graphical, or
verbal descriptions of linear functions.
Step 1
First, input the equations
into the calculator using the
function
TEKS A.5C
(Objective 3)
• equation
• relationship
• table of values
• ordered pair
Step 2
Look at the tables of
values for all equations:
Step 3
Check the first ordered
pair (-6, 23) from the original table. As you
can see, that point is included in all four
tables.
Continue checking the rest of the ordered
pairs.
Only Y1 includes all points from the table.
Thus, letter F is the correct answer.
Objective 3
2008
TEKS Tech Cards
What is the slope of the line that contains the
coordinate points (8, −3) and (−2, 7)?
A)
B)
C)
D)
-1
-9/11
-5/3
-2/5
[TEKS A.6A : 2006 #17 ] STUDENT EXPECTATION
The student develops the concept of slope as rate of change and
determines slopes from graphs, tables, and algebraic representations.
Step 1
TEKS A.6A
Guide students to write the
(Objective 3)
slope formula, which can be found in their
formula chart:
m =y2-y1
x2-x1
Identify the x and y values of the given
• Slope
points: (8, −3) (−2, 7)
• line
x1 y1
x2 y2
Calculate y2-y1:
Calculate x2-x1:
Step 2
=10
=-10
• coordinate points
• equation
Find the slope:
So, m=-1
Extend by finding the equation of the line
that goes through the given points and has
the obtained slope.
Step 3
Graph the equation
Objective 3
2008
TEKS Tech Cards
Find the slope of the given line.
A
9
B
3
C

D
-3
[TEKS A.6A ] STUDENT EXPECTATION
The student develops the concept of slope as rate of change and
determines slopes from graphs, tables, and algebraic representations
Step 1
Begin by plotting two
points from the graph (0, 2) and (-2, -4)
TEKS A.6A
(Objective 3)
• slope
• line
• parallel
Step 2
If letter A is the correct
answer, then the slope of the line must be
9. So, we can graph the equation y=9x
and see if such line passes through the
points or seems parallel to the line that
would go through those points.
It doesn't. Thus,
letter A is not the
Step 3
If we continue this
process, we can see that letter B is the
right answer (Look at the graphs below).
B) y=3x
C) y=1/3 x
D) y= -3x
Objective 3
2008
TEKS Tech Cards
What are the x- and y-intercepts of the function
graphed below?
A
B
C
D
(4, 0) and (5, 0)
(4, 0) and (0, 5)
(0, 4) and (5, 0)
(0, 4) and (0, 5)
[TEKS A.3B : 2004 #42 ] STUDENT EXPECTATION
Given situations, the student looks for patterns and represents
generalizations algebraically.
Step 1
Find the equations of the
lines passing through the given points in the
answer choices and graph them:
A) (4,0) & (5,0)
TEKS A.3B
(Objective 3)
• x-intercept
• y-intercept
• function
• line
• points
Step 2
We continue the same
process using the rest of the answer choices
B) (4,0) & (0,5)
Step 3
C) (0,4) & (5,0)
D) (0,4) & (0,5)
We can see that letter B is correct because:
1) The graphs match
2) (4,0) is the x-intercept on the graph, and
3) (0,5) is the y-intercept on the graph.
Objective 3
2008
TEKS Tech Cards
Which linear function includes the points (–3, 1) and
(–2, 4)?
A
B
C
D
f(x) = 3x + 10
f(x) = ⅓ x + 2
f(x) = 3x − 6
f(x) = −3x + 1
[TEKS A.6D : 2003#44 ] STUDENT EXPECTATION
The student graphs and writes equations of lines given characteristics
such as two points, a point and a slope, or a slope and -intercept.
Step 1
Begin by plotting the
given points (-3, 1) and (-2, 4).
TEKS A.6D
(Objective 3)
• linear function
• point
• equation
Step 2
Graph each function to
examine which one passes through the
plotted points.
A. f(x) = 3x + 10
y = 3x + 10
Step 3
Similarly:
B. y = ⅓ x + 2 C. y= 3x − 6 D y= −3x + 1
Thus, the correct answer is letter A.
Objective 4
2008
TEKS Tech Cards
The graphs of the linear equations y = 2x – 3 and
y = 3x − 7 are shown below.
If 2x − 3 = 3x − 7, what is the value of x?
A
B
C
D
4
5
9
10
[TEKS A.7B : 2004 #36 ] STUDENT EXPECTATION
The student investigates methods for solving linear equations and
inequalities using [concrete] models, graphs, and the properties of
equality, selects a method, and solves the equations and inequalities.
Step 1
The correct value of x will
make the equation 2x-3 = 3x -7 true. Guess
and check to see which answer choice will do
that.
A) x=4
TEKS A.7B
(Objective 4)
• graph
• linear equation
• true statement
A 1 represents a true statement. Therefore,
A is the correct answer.
Step 2
However, to confirm that A
is the right choice, we must test the rest of
B) x=5
Notice how the calculator produced a 0 for
this choice. Thus, this answer cannot
represent the correct value for x.
Step 3
C) x=9
D) x=10
Similarly,
Objective 10
2008
TEKS Tech Cards
Alonso’s family rented a car when they flew to
Orlando for a 4-day vacation. They paid \$39 per
day and \$0.09 for each mile driven. How much
did it cost to rent the car for 4 days and drive 350
miles, not including tax?
A
B
C
D
\$70.50
\$124.50
\$156.00
\$187.50
[TEKS 8.14B: 2003 #5 ] STUDENT EXPECTATION
The student uses a problem-solving model that incorporates
understanding the problem, making a plan, carrying out the plan, and
evaluating the solution for reasonableness
Step 1
Begin by writing an
equation that describes the situation:
C = 39 d + 0.09 m
C  Total Cost
d  Number of days
TEKS 8.14B
(Objective 10)
• equation
• given values
• solution
m  Miles driven
Step 2
Store the given values for d and m:
Step 3
Enter the equation and
find a solution:
Therefore, the correct answer is letter D.
Objective 6
2008
TEKS Tech Cards
Jake made a map of his neighborhood for a school
project. He placed a grid over the map.
Which coordinate point best represents the post
office?
A
(6, 12)
B
(12, 6)
C
(1.2, 0.6)
D
(0.6, 1.2)
[TEKS 8.7D: 2003#43 ] STUDENT EXPECTATION
The student will locate and name points on a coordinate plane using
ordered pairs of rational numbers
Step 1
Adjust the window to
match the one on the given grid:
TEKS 8.7D
(Objective 6)
• point
• coordinate
• grid
• ordered pair
Step 2
Plot the ordered pairs for
A)
Similarly,
B)
Step 3
C)
D)
The answer choice that shows a point
representing the post office is letter D.
Objective 4
2008
TEKS Tech Cards
Which inequality best describes the graph shown
below?
A
B
C
D
y ≥ −2x
y ≥ −x − 2
y ≥ −2x − 2
y≥x–2
[TEKS A.7A ] STUDENT EXPECTATION
The student analyzes situations involving linear functions and
formulates linear equations or inequalities to solve problems.
Step 1
A)
Graph each inequality:
TEKS A.7A
(Objective 4)
B)
• inequality
• table of values
• intercepts
Step 2
C)
D)
You can eliminate answer choices A and D
Step 3
Check the tables of values
for choices B and C:
B)
C)
Choice C does include the intercepts (-2, 0)
and (0, -2). Thus, C is the correct answer.
Objective 1
2008
TEKS Tech Cards
Which inequality best describes the graph shown
below?
F
G
H
J
y > − ¾x + 5
y < − 4⁄3 x + 5
y < − ¾x + 5
y > − 4⁄3 x + 5
[TEKS A.1D : 2006 #5 ] STUDENT EXPECTATION
The student represents relationships among quantities using
[concrete] models, tables, graphs, diagrams, verbal descriptions,
equations, and inequalities.
Step 1
Begin by selecting a point
from the shaded area. For example (8, -2)
Store the corresponding x and y values.
Step 2
F)
• inequality
• point
• corresponding values
Test each inequality:
G)
H)
J)
F and G produced a 0 (False statements!)
Step 3
We repeat the process for
H and J, only, using a different point:
(5, 3)
H)
TEKS A.1D
(Objective 1)
J)
H produced a false statement. Therefore,
letter J is the correct answer.
Objective 5
2008
TEKS Tech Cards
Which expression describes the area in square
units of a rectangle that has a width of 4x 3y 2
and a length of 3x 2y 3?
A
B
C
D
12x 6y 6
12x 5y 5
7x 6y 6
7x 5y 5
[TEKS A.11A : 2003 #10 ] STUDENT EXPECTATION
The student uses [patterns to generate] the laws of exponents and
applies them in problem solving situations.
Step 1
Begin by storing a value
for both x and y:
TEKS A.11A
(Objective 5)
• expression • width
• area
• length
• square units
• rectangle
Step 2
Find the area of the
rectangle by multiplying the given
expressions:
A= (L)(W) A=
Step 3
Input all choices and
compare to the value obtained in step 2:
A)
B)
C)
D)
The correct
answer is letter B
since
=
Objective 5
2008
TEKS Tech Cards
Which expression is equivalent to
A
B
C
D
4x 9
4x 2
2x 8
2x 4
[TEKS A.11A : 2006 #9 ] STUDENT EXPECTATION
The student uses [patterns to generate] the laws of exponents and
applies them in problem solving situations.
Step 1
Enter the expression into
the calculator using the y editor:
TEKS A.11A
(Objective 5)
• expression
• equivalent
• table of values
Step 2
Enter each answer choice
and compare the tables of values
A)
B)
Step 3
C)
D)
Objective 10
2008
TEKS Tech Cards
Sean is an Algebra I student who believes that
xy 2 = (xy) 2. Rudy informs Sean that this theory is
not always true. Which pair of values for x and y
could Rudy use to disprove Sean’s theory?
F
G
H
J
x = 0 and y = 2
x = 1 and y = 2
x = 2 and y = 0
x = 2 and y = 1
[TEKS 8.16B : 2004 #28 ] STUDENT EXPECTATION
The student validates his/her conclusions using mathematical
properties and relationships.
Step 1
Substitute the x and y
values from each answer choice into each
side of the equation and compare.
F) x=0 and y=2
xy 2
(xy) 2
TEKS 8.16B
(Objective 10)
• pair
• values
• substitute
• equation
Step 2
G) x=1 and y=2
xy 2
(xy) 2
H) x=2 and y=0
xy 2
(xy) 2
Step 3
J) x=2 and y=1
xy 2
(xy) 2
The only choice that Rudy could use to
disprove Sean is letter J.
Objective 5
2008
TEKS Tech Cards
If y = x 3, what is equivalent to x 12 ?
A
B
C
D
y 36
y 15
y9
y4
[TEKS A.11A : 2004 #44 ] STUDENT EXPECTATION
The student uses [patterns to generate] the laws of exponents and
applies them in problem solving situations.
Step 1
Input both
using the y editor.
y=x3
and
x12
TEKS A.11A
(Objective 5)
• equation
• equivalent
• table of values
Step 2
Input the answer choices
and compare their tables of values with that
of x12
A)
Step 3
B)
C)
D)
Similarly,
Objective 7
2008
TEKS Tech Cards
A 12- by 16-foot rectangular floor will be
covered by square tiles that measure 2 feet on
each side. If the tiles are not cut, how many of
them will be needed to cover the floor?
A
B
C
D
192
96
48
14
[TEKS 8.7B : 2003 #31 ] STUDENT EXPECTATION
The student uses geometric concepts and properties to solve
problems in fields such as art and architecture.
Step 1
Adjust the window :
TEKS 8.7B
(Objective 7)
• rectangular floor
• square tiles
• measure
• cover
• grid
Step 2
Turn on the grid and graph:
Step 3
There are 6 “tiles” in each column and 8
“tiles” in each row. Therefore, the total
number of tiles needed to cover the floor is:
Thus, the correct answer is C.
Objective 2
2008
TEKS Tech Cards
Simplify the algebraic expression 3(x + 3) − 2(x + 3).
A
B
C
D
x+3
x−3
−6x2 − 54
6x2 + 3
[TEKS A.4B : 2004 #20 ] STUDENT EXPECTATION
The student uses the commutative, associative, and distributive
properties to simplify algebraic expressions.
Step 1
Input the expression
using the
and graph:
TEKS A.4B
(Objective 2)
•simplify
•algebraic Expression
Step 2
Graph all choices:
Similarly,
A
B
Step 3
C
D
Notice how letter A is the only answer
which graph matches the original one.
Thus, letter A is the correct answer.
Objective 3
2008
TEKS Tech Cards
Which of the following ordered pairs is the
x-intercept or the y-intercept of the function
2x − y = 8?
F
G
H
J
(8, 0)
(0, 4)
(4, 0)
(0, 8)
[TEKS A.6E : 2006 #19 ] STUDENT EXPECTATION
The student determines the intercepts of linear functions from graphs,
tables, and algebraic representations.
Step 1
Find the x-intercept:
Substitute a 0 for y
2x-0=8
• ordered pair
• x-intercept
• y-intercept
• function
• solve
Solve:
The x-intercept is at
x=4, or (4, 0)
Step 2
TEKS A.6E
(Objective 3)
Find the y-intercept:
Substitute a 0 for x
2(0)-y=8
Solve similarly. Continue to use x when
you input the expression into the calculator
Scroll up until you
see y1=y2
Step 3
So,
The x-intercept is (4, 0), and
The y-intercept is (0, -8)
Therefore, the correct answer is letter H.