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Math Problems
Algebra 1
Slopes of parallel and perpendicular lines
The line represented by the equation
−
x
3.5
+
y
12.5
=
1
-\frac{x}{3.5}+\frac{y}{12.5}=1
−
3.5
x
+
12.5
y
=
1
is graphed in the
x
y
x y
x
y
-plane. Which of the following statements correctly describes the graph of the line?
\newline
Choose
1
1
1
answer:
\newline
(A) The line has a slope of
12
12
12
.
5
5
5
.
\newline
(B) The line goes through the point
(
3.5
,
12.5
)
(3.5,12.5)
(
3.5
,
12.5
)
.
\newline
(C) The line has a positive
x
x
x
intercept and a negative
y
y
y
intercept.
\newline
(D) The line has a negative
x
x
x
intercept and a positive
y
y
y
intercept.
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Two lines graphed in the
x
y
x y
x
y
-plane have the equations
2
x
+
5
y
=
20
2 x+5 y=20
2
x
+
5
y
=
20
and
y
=
k
x
−
3
y=k x-3
y
=
k
x
−
3
, where
k
k
k
is a constant. For what value of
k
k
k
will the two lines be perpendicular?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
5
-\frac{2}{5}
−
5
2
\newline
(B)
2
5
\frac{2}{5}
5
2
\newline
(C)
5
2
\frac{5}{2}
2
5
\newline
(D)
−
5
2
-\frac{5}{2}
−
2
5
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A circle in the
x
y
x y
x
y
-plane has the equation
\newline
(
x
−
4
)
2
+
(
y
+
1
)
2
=
16
(x-4)^{2}+(y+1)^{2}=16
(
x
−
4
)
2
+
(
y
+
1
)
2
=
16
. Which of the following points does NOT lie inside the circle?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
7
,
−
3
)
(7,-3)
(
7
,
−
3
)
\newline
(B)
(
4
,
−
1
)
(4,-1)
(
4
,
−
1
)
\newline
(C)
(
2
,
2
)
(2,2)
(
2
,
2
)
\newline
(D)
(
0
,
0
)
(0,0)
(
0
,
0
)
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Line
q
q
q
has a slope of
−
2
3
\frac{-2}{3}
3
−
2
. Line
r
r
r
is perpendicular to
q
q
q
. What is the slope of line
r
r
r
?
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