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Math Problems
Algebra 1
Write an equation for a parallel or perpendicular line
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
s
s
s
is line
t
t
t
, which passes through the point
(
−
1
,
3
)
(-1,3)
(
−
1
,
3
)
. What is the equation of line
t
t
t
?
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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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Example
1
1
1
\newline
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
?
\newline
Step
1
1
1
: Identify given slope line
f
:
y
=
2
x
+
3
f: y=2 x+3
f
:
y
=
2
x
+
3
\newline
Step
2
2
2
: Identify new slope
\newline
line
g
:
m
=
2
g: m=2
g
:
m
=
2
\newline
Step
3
3
3
: Determine new
y
y
y
-intercept
6
=
2
(
5
)
+
b
6=2(5)+b
6
=
2
(
5
)
+
b
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
0
0
0
\newline
6
−
10
=
10
+
b
−
10
−
4
=
b
\begin{aligned} 6-10 & =10+b-10 \\ -4 & =b \end{aligned}
6
−
10
−
4
=
10
+
b
−
10
=
b
\newline
Step
4
4
4
: Write new equation line
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
1
1
1
and simplify to
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
2
2
2
equals two
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
3
3
3
minus four.
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Parallelogram
W
D
N
B
W D N B
W
D
NB
is shown where
W
D
=
12
W D=12
W
D
=
12
inches (in.),
B
R
=
4
B R=4
BR
=
4
in.,
N
R
=
10
N R=10
NR
=
10
in., and
D
N
=
6
D N=6
D
N
=
6
in.
\newline
Which expression can be used to determine the area of WDNB?
\newline
(A)
6
⋅
10
6 \cdot 10
6
⋅
10
\newline
(B)
6
⋅
12
6 \cdot 12
6
⋅
12
\newline
(C)
1
2
(
10
)
(
4
)
\frac{1}{2}(10)(4)
2
1
(
10
)
(
4
)
\newline
(D)
12
+
10
+
6
+
4
12+10+6+4
12
+
10
+
6
+
4
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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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What is the equation of the line graphed in the
x
y
x y
x
y
-plane that passes through the point
(
6
,
3
)
(6,3)
(
6
,
3
)
and is perpendicular to the line whose equation is
y
=
−
3
x
+
5
y=-3 x+5
y
=
−
3
x
+
5
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
3
x
+
1
3
y=3 x+\frac{1}{3}
y
=
3
x
+
3
1
\newline
(B)
y
=
1
3
x
+
5
y=\frac{1}{3} x+5
y
=
3
1
x
+
5
\newline
(C)
y
=
1
3
x
+
1
y=\frac{1}{3} x+1
y
=
3
1
x
+
1
\newline
(D)
y
=
−
3
x
+
3
y=-3 x+3
y
=
−
3
x
+
3
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The equation
6
y
+
12
x
=
18
6 y+12 x=18
6
y
+
12
x
=
18
is graphed in the
x
y
x y
x
y
-plane. Which of the following equations has a graph that is perpendicular to the graph of the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
2
x
+
3
y=-2 x+3
y
=
−
2
x
+
3
\newline
(B)
y
=
1
2
x
+
3
y=\frac{1}{2} x+3
y
=
2
1
x
+
3
\newline
(C)
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
\newline
(D)
y
=
−
1
2
x
+
3
y=-\frac{1}{2} x+3
y
=
−
2
1
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
2
,
2
)
\left(-\frac{1}{2}, 2\right)
(
−
2
1
,
2
)
and is parallel to the line with equation
y
=
−
8
x
+
3
y=-8 x+3
y
=
−
8
x
+
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
1
8
x
+
4
y=\frac{1}{8} x+4
y
=
8
1
x
+
4
\newline
(B)
y
=
1
8
x
+
1
y=\frac{1}{8} x+1
y
=
8
1
x
+
1
\newline
(C)
y
=
−
8
x
−
2
y=-8 x-2
y
=
−
8
x
−
2
\newline
(D)
y
=
−
8
x
+
2
y=-8 x+2
y
=
−
8
x
+
2
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Which of the following is the equation of the line
A
A
A
graphed in the
x
y
x y
x
y
-plane that passes through the point
(
−
2
,
2
)
(-2,2)
(
−
2
,
2
)
and is parallel to the line
B
B
B
whose equation is
y
−
3
=
0
y-3=0
y
−
3
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
+
2
=
0
y+2=0
y
+
2
=
0
\newline
(B)
x
+
2
=
0
x+2=0
x
+
2
=
0
\newline
(C)
y
−
2
=
0
y-2=0
y
−
2
=
0
\newline
(D)
x
−
2
=
0
x-2=0
x
−
2
=
0
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Line
p
p
p
has an equation of
y
=
−
8
x
+
6
y = -8x + 6
y
=
−
8
x
+
6
. Line
q
q
q
, which is perpendicular to line
p
p
p
, includes the point
(
2
,
−
2
)
(2, -2)
(
2
,
−
2
)
. 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.
\newline
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