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Math Problems
Algebra 1
Point-slope form: write an equation
Let
g
(
x
)
=
cos
(
x
)
g(x) = \cos(x)
g
(
x
)
=
cos
(
x
)
. Can we use the intermediate value theorem to say the equation
g
(
x
)
=
0.8
g(x) = 0.8
g
(
x
)
=
0.8
has a solution where
0
≤
x
≤
π
2
0 \leq x \leq \frac{\pi}{2}
0
≤
x
≤
2
π
?
\newline
Choose
1
1
1
answer:
\newline
(Choice A) No, since the function is not continuous on that interval.
\newline
A No, since the function is not continuous on that interval.
\newline
(Choice B) No, since
0.8
0.8
0.8
is not between
g
(
0
)
g(0)
g
(
0
)
and
g
(
π
2
)
g\left(\frac{\pi}{2}\right)
g
(
2
π
)
.
\newline
B No, since
0.8
0.8
0.8
is not between
g
(
0
)
g(0)
g
(
0
)
and
g
(
π
2
)
g\left(\frac{\pi}{2}\right)
g
(
2
π
)
.
\newline
(Choice C) Yes, both conditions for using the intermediate value theorem have been met.
\newline
C Yes, both conditions for using the intermediate value theorem have been met.
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Brenna is taking a trip on a train to visit her cousins. The function
y
=
−
60
x
+
220
y = -60x + 220
y
=
−
60
x
+
220
represents the number of miles to Brenna's destination,
y
y
y
, depending on how many hours she has been on the train,
x
x
x
.
\newline
What is true about the function?
\newline
Choices:
\newline
(A)It is linear because the rate of change stays the same.
\newline
(B)It is linear because the rate of change is decreasing.
\newline
(C)It is nonlinear because the rate of change stays the same.
\newline
(D)It is nonlinear because the rate of change is decreasing.
Get tutor help
A line with a slope of
−
5
-5
−
5
passes through the point
(
1
,
6
)
(1,6)
(
1
,
6
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line with a slope of
−
9
-9
−
9
passes through the point
(
7
,
9
)
(7,9)
(
7
,
9
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
−
9
,
−
6
)
(-9,-6)
(
−
9
,
−
6
)
has a slope of
−
5
-5
−
5
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
−
5
,
1
)
(-5,1)
(
−
5
,
1
)
and has a slope of
4
4
4
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
4
,
5
)
(4,5)
(
4
,
5
)
and has a slope of
−
1
7
-\frac{1}{7}
−
7
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line with a slope of
−
2
-2
−
2
passes through the point
(
7
,
−
3
)
(7,-3)
(
7
,
−
3
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
−
5
,
−
8
)
(-5,-8)
(
−
5
,
−
8
)
and has a slope of
−
5
-5
−
5
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
−
7
,
−
6
)
(-7,-6)
(
−
7
,
−
6
)
and has a slope of
1
5
\frac{1}{5}
5
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line with a slope of
−
4
-4
−
4
passes through the point
(
9
,
9
)
(9,9)
(
9
,
9
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line with a slope of
−
1
4
-\frac{1}{4}
−
4
1
passes through the point
(
3
,
4
)
(3,4)
(
3
,
4
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line with a slope of
−
1
7
-\frac{1}{7}
−
7
1
passes through the point
(
−
1
,
9
)
(-1,9)
(
−
1
,
9
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
10
,
5
)
(10,5)
(
10
,
5
)
and has a slope of
5
5
5
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line has a slope of
−
3
-3
−
3
and passes through the point
(
3
,
4
)
(3,4)
(
3
,
4
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
8
,
7
)
(8,7)
(
8
,
7
)
has a slope of
−
10
-10
−
10
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
4
,
8
)
(4,8)
(
4
,
8
)
has a slope of
−
4
-4
−
4
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
8
,
−
3
)
(8,-3)
(
8
,
−
3
)
has a slope of
−
1
10
-\frac{1}{10}
−
10
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
−
8
,
−
8
)
(-8,-8)
(
−
8
,
−
8
)
has a slope of
−
3
-3
−
3
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
−
10
,
4
)
(-10,4)
(
−
10
,
4
)
has a slope of
−
1
8
-\frac{1}{8}
−
8
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
6
,
−
3
)
(6,-3)
(
6
,
−
3
)
and has a slope of
−
3
-3
−
3
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
4
,
−
6
)
(4,-6)
(
4
,
−
6
)
has a slope of
−
1
5
-\frac{1}{5}
−
5
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
3
,
1
)
(3,1)
(
3
,
1
)
has a slope of
−
7
-7
−
7
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
4
,
3
)
(4,3)
(
4
,
3
)
and has a slope of
−
8
-8
−
8
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
6
,
3
)
(6,3)
(
6
,
3
)
has a slope of
7
7
7
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
A line that includes the point
(
−
9
,
5
)
(-9,5)
(
−
9
,
5
)
has a slope of
−
3
-3
−
3
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
y -
y
−
______
=
=
=
______
(
x
−
(x -
(
x
−
______
)
)
)
Get tutor help
There is a line that includes the point
(
10
,
9
)
(10,9)
(
10
,
9
)
and has a slope of
−
1
8
-\frac{1}{8}
−
8
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
−
4
,
−
2
)
(-4,-2)
(
−
4
,
−
2
)
has a slope of
10
10
10
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
There is a line that includes the point
(
4
,
4
)
(4,4)
(
4
,
4
)
and has a slope of
−
8
-8
−
8
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
−
2
,
10
)
(-2,10)
(
−
2
,
10
)
has a slope of
−
1
7
-\frac{1}{7}
−
7
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line with a slope of
1
6
\frac{1}{6}
6
1
passes through the point
(
8
,
−
4
)
(8,-4)
(
8
,
−
4
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
=
_
_
_
_
_
(
x
−
_
_
_
_
_
)
y - \_\_\_\_\_ = \_\_\_\_\_(x - \_\_\_\_\_)
y
−
_____
=
_____
(
x
−
_____
)
Get tutor help
A line has a slope of
1
5
\frac{1}{5}
5
1
and passes through the point
(
−
5
,
3
)
(-5,3)
(
−
5
,
3
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
=
_
_
_
_
_
(
x
−
_
_
_
_
_
)
y - \_\_\_\_\_ = \_\_\_\_\_(x - \_\_\_\_\_)
y
−
_____
=
_____
(
x
−
_____
)
Get tutor help
A line that includes the point
(
9
,
4
)
(9,4)
(
9
,
4
)
has a slope of
1
10
\frac{1}{10}
10
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
−
5
,
−
6
)
(-5,-6)
(
−
5
,
−
6
)
has a slope of
1
7
\frac{1}{7}
7
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line with a slope of
−
1
9
-\frac{1}{9}
−
9
1
passes through the point
(
−
3
,
6
)
(-3,6)
(
−
3
,
6
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line with a slope of
1
4
\frac{1}{4}
4
1
passes through the point
(
−
8
,
−
8
)
(-8,-8)
(
−
8
,
−
8
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line has a slope of
1
5
\frac{1}{5}
5
1
and passes through the point
(
−
7
,
−
3
)
(-7,-3)
(
−
7
,
−
3
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
_
=
_
_
_
_
_
_
(
x
−
_
_
_
_
_
_
)
y - \_\_\_\_\_\_ = \_\_\_\_\_\_(x - \_\_\_\_\_\_)
y
−
______
=
______
(
x
−
______
)
Get tutor help
A line with a slope of
−
1
6
-\frac{1}{6}
−
6
1
passes through the point
(
10
,
3
)
(10,3)
(
10
,
3
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
−
6
,
−
1
)
(-6,-1)
(
−
6
,
−
1
)
has a slope of
1
3
\frac{1}{3}
3
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line has a slope of
1
9
\frac{1}{9}
9
1
and passes through the point
(
7
,
3
)
(7,3)
(
7
,
3
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
_
=
_
_
_
_
_
_
(
x
−
_
_
_
_
_
_
)
y - \_\_\_\_\_\_ = \_\_\_\_\_\_(x - \_\_\_\_\_\_)
y
−
______
=
______
(
x
−
______
)
Get tutor help
A line has a slope of
1
2
\frac{1}{2}
2
1
and passes through the point
(
2
,
−
1
)
(2,-1)
(
2
,
−
1
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
=
_
_
_
_
_
(
x
−
_
_
_
_
_
)
y - \_\_\_\_\_ = \_\_\_\_\_(x - \_\_\_\_\_)
y
−
_____
=
_____
(
x
−
_____
)
Get tutor help
A line that includes the point
(
2
,
1
)
(2,1)
(
2
,
1
)
has a slope of
−
1
3
-\frac{1}{3}
−
3
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
There is a line that includes the point
(
4
,
5
)
(4,5)
(
4
,
5
)
and has a slope of
7
7
7
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
7
,
9
)
(7,9)
(
7
,
9
)
has a slope of
−
8
-8
−
8
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line that includes the point
(
3
,
9
)
(3,9)
(
3
,
9
)
has a slope of
−
4
-4
−
4
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line with a slope of
8
8
8
passes through the point
(
−
8
,
2
)
(-8,2)
(
−
8
,
2
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
_
=
_
_
_
_
_
_
(
x
−
_
_
_
_
_
_
)
y - \_\_\_\_\_\_ = \_\_\_\_\_\_(x - \_\_\_\_\_\_)
y
−
______
=
______
(
x
−
______
)
Get tutor help
A line has a slope of
2
2
2
and passes through the point
(
3
,
−
2
)
(3,-2)
(
3
,
−
2
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
=
_
_
_
_
_
(
x
−
_
_
_
_
_
)
y - \_\_\_\_\_ = \_\_\_\_\_(x - \_\_\_\_\_)
y
−
_____
=
_____
(
x
−
_____
)
Get tutor help
A line that includes the point
(
−
8
,
10
)
(-8,10)
(
−
8
,
10
)
has a slope of
3
3
3
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
There is a line that includes the point
(
−
8
,
10
)
(-8,10)
(
−
8
,
10
)
and has a slope of
1
10
\frac{1}{10}
10
1
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
‾
=
‾
(
x
−
‾
)
y - \underline{\quad} = \underline{\quad}(x - \underline{\quad})
y
−
=
(
x
−
)
Get tutor help
A line has a slope of
5
5
5
and passes through the point
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
. What is its equation in point-slope form?
\newline
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
\newline
y
−
_
_
_
_
_
=
_
_
_
_
_
(
x
−
_
_
_
_
_
)
y - \_\_\_\_\_ = \_\_\_\_\_(x - \_\_\_\_\_)
y
−
_____
=
_____
(
x
−
_____
)
Get tutor help
1
2
3
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