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Math Problems
Algebra 1
Write an equation for a parallel or perpendicular line
The equation of line
q
q
q
is
y
=
3
x
−
2
y = 3x - 2
y
=
3
x
−
2
. Line
r
r
r
is perpendicular to line
q
q
q
and passes through
(
1
,
3
)
(1,3)
(
1
,
3
)
. What is the equation of line
r
r
r
?
\newline
Write the equation in slope-intercept form.
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The equation for line
s
s
s
can be written as
y
=
3
10
x
+
8
y = \frac{3}{10}x + 8
y
=
10
3
x
+
8
. Line
t
t
t
is parallel to line
s
s
s
and passes through
(
−
7
,
−
2
)
(-7,-2)
(
−
7
,
−
2
)
. What is the equation of line
t
t
t
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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Line
t
t
t
has an equation of
y
=
10
x
−
8
y = 10x - 8
y
=
10
x
−
8
. Line
u
u
u
is perpendicular to line
t
t
t
and passes through
(
−
10
,
−
6
)
(-10,-6)
(
−
10
,
−
6
)
. What is the equation of line
u
u
u
?
\newline
Write the equation in slope-intercept form.
Get tutor help
The equation for line
u
u
u
can be written as
y
=
−
9
4
x
+
1
y = -\frac{9}{4}x + 1
y
=
−
4
9
x
+
1
. Line
v
v
v
, which is perpendicular to line
u
u
u
, includes the point
(
−
3
,
2
)
(-3,2)
(
−
3
,
2
)
. What is the equation of line
v
v
v
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation for line
v
v
v
can be written as
y
=
−
9
7
x
−
5
y = -\frac{9}{7}x - 5
y
=
−
7
9
x
−
5
. Line
w
w
w
, which is perpendicular to line
v
v
v
, includes the point
(
9
,
6
)
(9,6)
(
9
,
6
)
. What is the equation of line
w
w
w
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation for line
g
g
g
can be written as
y
=
7
2
x
+
6
y = \frac{7}{2}x + 6
y
=
2
7
x
+
6
. Line
h
h
h
includes the point
(
−
2
,
−
3
)
(-2,-3)
(
−
2
,
−
3
)
and is parallel to line
g
g
g
. What is the equation of line
h
h
h
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation for line
p
p
p
can be written as
y
=
−
1
2
x
+
8
y = -\frac{1}{2}x + 8
y
=
−
2
1
x
+
8
. Line
q
q
q
, which is perpendicular to line
p
p
p
, includes the point
(
4
,
7
)
(4,7)
(
4
,
7
)
. What is the equation of line
q
q
q
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation of line
v
v
v
is
y
=
9
x
+
1
y = 9x + 1
y
=
9
x
+
1
. Line
w
w
w
is perpendicular to line
v
v
v
and passes through
(
3
,
−
2
)
(3,-2)
(
3
,
−
2
)
. What is the equation of line
w
w
w
?
\newline
Write the equation in slope-intercept form.
Get tutor help
The equation of line
s
s
s
is
y
=
−
1
2
x
+
5
y = -\frac{1}{2}x + 5
y
=
−
2
1
x
+
5
. Line
t
t
t
includes the point
(
−
10
,
−
4
)
(-10,-4)
(
−
10
,
−
4
)
and is parallel to line
s
s
s
. What is the equation of line
t
t
t
? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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Line
g
g
g
has an equation of
y
=
1
3
x
−
1
y = \frac{1}{3}x - 1
y
=
3
1
x
−
1
. Parallel to line
g
g
g
is line
h
h
h
, which passes through the point
(
10
,
2
)
(10,2)
(
10
,
2
)
. What is the equation of line
h
h
h
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
The equation of line
v
v
v
is
y
=
x
+
1
7
y = x + \frac{1}{7}
y
=
x
+
7
1
. Parallel to line
v
v
v
is line
w
w
w
, which passes through the point
(
−
1
,
−
2
)
(-1,-2)
(
−
1
,
−
2
)
. What is the equation of line
w
w
w
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation for line
p
p
p
can be written as
y
=
9
7
x
−
9
y = \frac{9}{7}x - 9
y
=
7
9
x
−
9
. Line
q
q
q
is perpendicular to line
p
p
p
and passes through
(
9
,
−
6
)
(9,-6)
(
9
,
−
6
)
. What is the equation of line
q
q
q
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
The equation for line
c
c
c
can be written as
y
=
3
4
x
−
2
y = \frac{3}{4}x - 2
y
=
4
3
x
−
2
. Line
d
d
d
, which is perpendicular to line
c
c
c
, includes the point
(
6
,
−
3
)
(6,-3)
(
6
,
−
3
)
. What is the equation of line
d
d
d
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
Line
g
g
g
has an equation of
y
=
−
2
9
x
+
6
y = -\frac{2}{9}x + 6
y
=
−
9
2
x
+
6
. Parallel to line
g
g
g
is line
h
h
h
, which passes through the point
(
3
,
2
)
(3,2)
(
3
,
2
)
. What is the equation of line
h
h
h
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
Line
v
v
v
has an equation of
y
=
−
2
x
+
5
y = -2x + 5
y
=
−
2
x
+
5
. Perpendicular to line
v
v
v
is line
w
w
w
, which passes through the point
(
6
,
−
5
)
(6,-5)
(
6
,
−
5
)
. What is the equation of line
w
w
w
?
\newline
Write the equation in slope-intercept form.
Get tutor help
Line
v
v
v
has an equation of
y
=
8
x
+
2
y = 8x + 2
y
=
8
x
+
2
. Line
w
w
w
is parallel to line
v
v
v
and passes through
(
−
1
,
−
2
)
(-1,-2)
(
−
1
,
−
2
)
. What is the equation of line
w
w
w
?
\newline
Write the equation in slope-intercept form.
Get tutor help
Line
p
p
p
has an equation of
y
=
−
5
6
x
−
5
y = -\frac{5}{6}x - 5
y
=
−
6
5
x
−
5
. Line
q
q
q
includes the point
(
9
,
−
4
)
(9,-4)
(
9
,
−
4
)
and is parallel to line
p
p
p
. What is the equation of line
q
q
q
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation of line
g
g
g
is
y
=
6
x
−
7
y = 6x - 7
y
=
6
x
−
7
. Line
h
h
h
, which is parallel to line
g
g
g
, includes the point
(
1
,
1
)
(1,1)
(
1
,
1
)
. What is the equation of line
h
h
h
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
The equation for line
p
p
p
can be written as
y
=
−
5
4
x
−
6
y = -\frac{5}{4}x - 6
y
=
−
4
5
x
−
6
. Line
q
q
q
includes the point
(
5
,
−
8
)
(5,-8)
(
5
,
−
8
)
and is parallel to line
p
p
p
. What is the equation of line
q
q
q
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
The equation for line
c
c
c
can be written as
y
=
−
6
7
x
−
1
y= -\frac{6}{7}x-1
y
=
−
7
6
x
−
1
. Line
d
d
d
is parallel to line
c
c
c
and passes through
(
10
,
−
9
)
(10, -9)
(
10
,
−
9
)
. What is the equation of line
d
d
d
?
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The equation for line
p
p
p
can be written as
y
=
9
7
x
−
9
y=\frac{9}{7}x-9
y
=
7
9
x
−
9
. Line
q
q
q
is perpendicular to line
p
p
p
and passes through
(
9
,
−
6
)
(9,-6)
(
9
,
−
6
)
. What is the equation of line
q
q
q
?
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The equation for line
u
u
u
can be written as
y
=
−
2
x
+
10
y = -2x + 10
y
=
−
2
x
+
10
. Line
v
v
v
, which is parallel to line
u
u
u
, includes the point
(
−
1
,
2
)
(-1, 2)
(
−
1
,
2
)
. What is the equation of line
v
v
v
?
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Which of the following is an equation of the line graphed in the
x
y
xy
x
y
plane that passes through the point
(
−
1
,
3.5
)
(-1,3.5)
(
−
1
,
3.5
)
and is perpendicular to the line
B
B
B
whose equation is
x
+
4.5
=
0
x+4.5=0
x
+
4.5
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\text{(A)}
(A)
x
=
−
1
x=-1
x
=
−
1
\newline
(B)
\text{(B)}
(B)
x
=
3.5
x=3.5
x
=
3.5
\newline
(C)
\text{(C)}
(C)
y
=
3.5
y=3.5
y
=
3.5
\newline
(D)
\text{(D)}
(D)
y
=
4.5
y=4.5
y
=
4.5
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The equation
3
x
−
2
y
=
4
3x-2y=4
3
x
−
2
y
=
4
is graphed in the
x
y
xy
x
y
-plane. Which of the statements is true of its graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph is a line parallel to the line whose equation is
y
=
−
2
3
x
+
1
y=-\frac{2}{3}x+1
y
=
−
3
2
x
+
1
.
\newline
(B) The graph is a line perpendicular to the line whose equation is
y
=
−
2
3
x
+
1
y=-\frac{2}{3}x+1
y
=
−
3
2
x
+
1
.
\newline
(C) The graph is a line with a slope of
−
2
3
-\frac{2}{3}
−
3
2
.
\newline
(D) The graph is a line with a slope of
−
3
2
-\frac{3}{2}
−
2
3
.
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The equation for line
j
j
j
can be written as
y
+
5
=
5
(
x
+
5
)
y+5=5(x+5)
y
+
5
=
5
(
x
+
5
)
. Line
k
k
k
includes the point
(
5
,
3
)
(5,3)
(
5
,
3
)
and is perpendicular to line
j
j
j
. What is the equation of line
k
k
k
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
The equation for line
g
g
g
can be written as
y
+
6
=
−
7
4
(
x
−
6
)
y+6=-\frac{7}{4}(x-6)
y
+
6
=
−
4
7
(
x
−
6
)
. Line
h
h
h
is parallel to line
g
g
g
and passes through
(
6
,
−
7
)
(6,-7)
(
6
,
−
7
)
. What is the equation of line
h
h
h
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Get tutor help
Line
j
j
j
has an equation of
y
+
6
=
y+6=
y
+
6
=
6
(
x
−
1
)
6(x-1)
6
(
x
−
1
)
. Line
k
k
k
is perpendicular to line
j
j
j
and passes through
(
8
,
−
4
)
(8,-4)
(
8
,
−
4
)
. What is the equation of line
k
k
k
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation of line
p
p
p
is
y
+
5
=
y+5=
y
+
5
=
−
10
(
x
+
2
)
-10(x+2)
−
10
(
x
+
2
)
. Line
q
q
q
is perpendicular to line
p
p
p
and passes through
(
−
1
,
−
1
)
(-1,-1)
(
−
1
,
−
1
)
. What is the equation of line
q
q
q
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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The equation of line
k
k
k
is
y
+
10
=
y+10=
y
+
10
=
3
(
x
+
3
)
3(x+3)
3
(
x
+
3
)
. Perpendicular to line
k
k
k
is line
ℓ
\ell
ℓ
, which passes through the point
(
5
,
−
5
)
(5,-5)
(
5
,
−
5
)
. What is the equation of line
ℓ
\ell
ℓ
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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Line
j
j
j
has an equation of
y
=
−
9
7
x
+
10
7
y=-\frac{9}{7} x+\frac{10}{7}
y
=
−
7
9
x
+
7
10
. Line
k
k
k
is parallel to line
j
j
j
and passes through
(
−
4
,
4
)
(-4,4)
(
−
4
,
4
)
. What is the equation of line
k
k
k
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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Line
g
g
g
has an equation of
y
=
2
x
+
1
y=2 x+1
y
=
2
x
+
1
. Line
h
h
h
includes the point
(
−
5
,
2
)
(-5,2)
(
−
5
,
2
)
and is perpendicular to line
g
\mathrm{g}
g
. What is the equation of line
h
\mathrm{h}
h
?
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The equation of line
v
v
v
is
y
=
x
+
1
7
y=x+\frac{1}{7}
y
=
x
+
7
1
. Parallel to line
v
v
v
is line
w
w
w
, which passes through the point
(
−
1
,
−
2
)
(-1,-2)
(
−
1
,
−
2
)
. What is the equation of the w?
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The equation of line
k
k
k
is
y
−
2
=
1
2
(
x
−
6
)
y-2=\frac{1}{2}(x-6)
y
−
2
=
2
1
(
x
−
6
)
. Perpendicular to line
k
k
k
is line
ℓ
\ell
ℓ
, which passes through the point
(
−
1
,
−
6
)
(-1,-6)
(
−
1
,
−
6
)
. What is the equation of line
l
l
l
?
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The equation of line
f
f
f
is
y
−
7
=
3
10
(
x
−
4
)
y-7=\frac{3}{10}(x-4)
y
−
7
=
10
3
(
x
−
4
)
. Line
9
9
9
, which is parallel to line
f
f
f
, includes the point
(
10
,
4
)
(10,4)
(
10
,
4
)
. What is the equation of line
g
g
g
?
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The equation for line
s
s
s
can be written as
y
=
−
10
x
+
5
4
y=-10 x+\frac{5}{4}
y
=
−
10
x
+
4
5
. Parallel to line
5
5
5
is line
t
t
t
, which passes through the point
(
−
1
,
3
)
(-1,3)
(
−
1
,
3
)
. What is the equation of line
1
1
1
?
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Line
v
v
v
has an equation of
y
=
−
5
x
+
6
y=-5 x+6
y
=
−
5
x
+
6
. Line
w
w
w
includes the point
(
−
1
,
−
2
)
(-1,-2)
(
−
1
,
−
2
)
and is perpendicular to line
v
v
v
. What is the equation of line
w
w
w
?
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Line
v
v
v
has an equation of
y
=
−
1
5
x
+
9
y=-\frac{1}{5} x+9
y
=
−
5
1
x
+
9
. Line
w
w
w
includes the point
(
−
10
,
1
)
(-10,1)
(
−
10
,
1
)
and is parallel to line
v
v
v
. What is the equation of line w?
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The equation of line
u
u
u
is
2
x
+
9
y
=
5
2 x+9 y=5
2
x
+
9
y
=
5
. Line
v
v
v
is parallel to line
u
u
u
and passes through
(
−
9
,
−
5
)
(-9,-5)
(
−
9
,
−
5
)
. What is the equation of line
v
v
v
?
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Line
j
j
j
has an equation of
y
−
8
=
−
2
3
(
x
+
5
)
y-8=-\frac{2}{3}(x+5)
y
−
8
=
−
3
2
(
x
+
5
)
. Line
k
k
k
is perpendicular to line
j
j
j
and passes through
(
−
6
,
−
2
)
(-6,-2)
(
−
6
,
−
2
)
. What is the equation of line
k
k
k
?
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Line
ℓ
\ell
ℓ
has equation
y
=
x
−
3
y=x-3
y
=
x
−
3
. Find the distance between
ℓ
\ell
ℓ
and the point
E
(
−
1
,
3
)
E(-1,3)
E
(
−
1
,
3
)
.
\newline
Round your answer to the nearest tenth.
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Line
ℓ
\ell
ℓ
has equation
y
=
x
−
3
y=x-3
y
=
x
−
3
. Find the distance between
ℓ
\ell
ℓ
and the point
E
(
−
1
,
3
)
E(-1,3)
E
(
−
1
,
3
)
.
\newline
Round your answer to the nearest tenth
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The equation for line
f
f
f
can be written as
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
. Line
g
g
g
is parallel to line
f
f
f
and passes through the point
(
5
,
6
)
(5,6)
(
5
,
6
)
. What is the equation of line
g
g
g
?
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Which of the following is an equation of the line
A
A
A
graphed in the
x
y
x y
x
y
-plane that passes through the point
(
−
1
,
3.5
)
(-1,3.5)
(
−
1
,
3.5
)
and is perpendicular to the line
B
B
B
whose equation is
x
+
4.5
=
0
x+4.5=0
x
+
4.5
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
−
1
x=-1
x
=
−
1
\newline
(B)
x
=
3.5
x=3.5
x
=
3.5
\newline
(C)
y
=
3.5
y=3.5
y
=
3.5
\newline
(D)
y
=
4.5
y=4.5
y
=
4.5
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A line in the
x
y
x y
x
y
-plane passes through the point
(
4
,
−
1
)
(4,-1)
(
4
,
−
1
)
and is perpendicular to the line with equation
y
=
x
+
5
y=x+5
y
=
x
+
5
. Which of the following is an equation of the line ?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
x
+
3
y=x+3
y
=
x
+
3
\newline
(B)
y
=
x
−
3
y=x-3
y
=
x
−
3
\newline
(C)
y
=
−
x
+
3
y=-x+3
y
=
−
x
+
3
\newline
(D)
y
=
−
x
−
3
y=-x-3
y
=
−
x
−
3
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Which of the following is an equation of the line in the
x
y
x y
x
y
-plane that passes through the point
(
3
,
−
4
)
(3,-4)
(
3
,
−
4
)
and is perpendicular to the line with equation
y
=
1
4
x
−
7
y=\frac{1}{4} x-7
y
=
4
1
x
−
7
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
1
4
x
+
8
y=\frac{1}{4} x+8
y
=
4
1
x
+
8
\newline
(B)
y
=
1
4
x
−
8
y=\frac{1}{4} x-8
y
=
4
1
x
−
8
\newline
(C)
y
=
−
4
x
+
8
y=-4 x+8
y
=
−
4
x
+
8
\newline
(D)
y
=
−
4
x
−
8
y=-4 x-8
y
=
−
4
x
−
8
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What is the equation of the line graphed in the
x
y
x y
x
y
-plane that passes through the point
(
−
4
,
−
5
)
(-4,-5)
(
−
4
,
−
5
)
and is parallel to the line whose equation is
3
x
−
4
y
=
−
8
3 x-4 y=-8
3
x
−
4
y
=
−
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
4
3
x
+
10
y=-\frac{4}{3} x+10
y
=
−
3
4
x
+
10
\newline
(B)
y
=
3
4
x
−
2
y=\frac{3}{4} x-2
y
=
4
3
x
−
2
\newline
(C)
y
=
3
4
x
−
8
y=\frac{3}{4} x-8
y
=
4
3
x
−
8
\newline
(D)
y
=
−
4
3
x
−
8
y=-\frac{4}{3} x-8
y
=
−
3
4
x
−
8
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Which of the following is an equation of the line in the
x
y
x y
x
y
-plane that passes through the point
(
−
5
,
3
)
(-5,3)
(
−
5
,
3
)
and is perpendicular to the line with equation
y
=
−
1
8
x
+
6
y=-\frac{1}{8} x+6
y
=
−
8
1
x
+
6
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
1
8
x
+
43
y=-\frac{1}{8} x+43
y
=
−
8
1
x
+
43
\newline
(B)
y
=
8
x
+
43
y=8 x+43
y
=
8
x
+
43
\newline
(C)
y
=
−
1
8
x
−
43
y=-\frac{1}{8} x-43
y
=
−
8
1
x
−
43
\newline
(D)
y
=
8
x
−
43
y=8 x-43
y
=
8
x
−
43
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Which of the following is an equation of the line in the
x
y
x y
x
y
-plane that passes through the point
(
2
,
6
)
(2,6)
(
2
,
6
)
and is parallel to the line with equation
x
=
2
3
y
+
2
x=\frac{2}{3} y+2
x
=
3
2
y
+
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
2
3
x
+
3
y=-\frac{2}{3} x+3
y
=
−
3
2
x
+
3
\newline
(B)
y
=
−
2
3
x
−
3
y=-\frac{2}{3} x-3
y
=
−
3
2
x
−
3
\newline
(C)
y
=
3
2
x
+
3
y=\frac{3}{2} x+3
y
=
2
3
x
+
3
\newline
(D)
y
=
3
2
x
−
3
y=\frac{3}{2} x-3
y
=
2
3
x
−
3
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Which of the following is an equation of the line in the
x
y
x y
x
y
-plane that passes through the point
(
1
,
1
)
(1,1)
(
1
,
1
)
and is parallel to the line with equation
y
=
−
3
x
−
1
y=-3 x-1
y
=
−
3
x
−
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
1
3
x
+
4
y=\frac{1}{3} x+4
y
=
3
1
x
+
4
\newline
(B)
y
=
1
3
x
+
1
y=\frac{1}{3} x+1
y
=
3
1
x
+
1
\newline
(C)
y
=
−
3
x
+
4
y=-3 x+4
y
=
−
3
x
+
4
\newline
(D)
y
=
−
3
x
+
1
y=-3 x+1
y
=
−
3
x
+
1
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The equation
3
x
−
2
y
=
4
3 x-2 y=4
3
x
−
2
y
=
4
is graphed in the
x
y
x y
x
y
-plane. Which of the statements is true of its graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph is a line parallel to the line whose equation is
y
=
−
2
3
x
+
1
y=-\frac{2}{3} x+1
y
=
−
3
2
x
+
1
.
\newline
(B) The graph is a line perpendicular to the line whose equation is
\newline
y
=
−
2
3
x
+
1
.
y=-\frac{2}{3} x+1 \text {. }
y
=
−
3
2
x
+
1
.
\newline
(C) The graph is a line with a slope of
−
2
3
-\frac{2}{3}
−
3
2
.
\newline
(D) The graph is a line with a slope of
−
3
2
-\frac{3}{2}
−
2
3
.
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