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Math Problems
Grade 8
Write a linear equation from two points
Write the equation of the line that passes through the points
(
1
,
6
)
(1,6)
(
1
,
6
)
and
(
−
7
,
8
)
(-7,8)
(
−
7
,
8
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Which of the following equations represents a line that passes through the points
(
3
,
−
6
)
(3,-6)
(
3
,
−
6
)
and
(
9
,
−
4
)
(9,-4)
(
9
,
−
4
)
?
\newline
I.
y
=
1
3
x
−
7
y=\frac{1}{3} x-7
y
=
3
1
x
−
7
\newline
II.
x
−
3
y
=
21
x-3 y=21
x
−
3
y
=
21
\newline
Neither
\newline
I only
\newline
II only
\newline
I and II
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Which of the following equations represents a line that passes through the points
(
0
,
7
)
(0,7)
(
0
,
7
)
and
(
−
9
,
10
)
(-9,10)
(
−
9
,
10
)
?
\newline
I.
2
x
+
6
y
=
42
2 x+6 y=42
2
x
+
6
y
=
42
\newline
II.
y
=
−
1
3
x
+
7
y=-\frac{1}{3} x+7
y
=
−
3
1
x
+
7
\newline
Neither
\newline
I only
\newline
II only
\newline
I and II
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Which of the following equations represents a line that passes through the points
(
−
10
,
9
)
(-10,9)
(
−
10
,
9
)
and
(
5
,
0
)
(5,0)
(
5
,
0
)
?
\newline
I.
3
x
+
5
y
=
10
3 x+5 y=10
3
x
+
5
y
=
10
\newline
II.
y
=
−
3
5
x
+
3
y=-\frac{3}{5} x+3
y
=
−
5
3
x
+
3
\newline
Neither
\newline
I only
\newline
II only
\newline
I and II
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Which of the following equations represents a line that passes through the points
(
−
4
,
5
)
(-4,5)
(
−
4
,
5
)
and
(
6
,
0
)
(6,0)
(
6
,
0
)
?
\newline
I.
3
x
+
6
y
=
12
3 x+6 y=12
3
x
+
6
y
=
12
\newline
II.
y
=
−
1
2
x
+
4
y=-\frac{1}{2} x+4
y
=
−
2
1
x
+
4
\newline
Neither
\newline
I only
\newline
II only
\newline
I and II
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Find an expression which represents the sum of
(
4
x
−
7
y
)
(4 x-7 y)
(
4
x
−
7
y
)
and
(
−
2
x
+
y
)
(-2 x+y)
(
−
2
x
+
y
)
in simplest terms.
\newline
Answer:
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Which of the following expressions is equivalent to
\newline
106
×
3.7
106 \times 3.7
106
×
3.7
?
\newline
Choose
1
1
1
answer:
\newline
(A)
106
×
37
÷
10
106 \times 37 \div 10
106
×
37
÷
10
\newline
(B)
106
×
37
÷
100
106 \times 37 \div 100
106
×
37
÷
100
\newline
(C)
106
×
37
÷
1
,
000
106 \times 37 \div 1,000
106
×
37
÷
1
,
000
\newline
(D)
106
×
37
÷
10
,
000
106 \times 37 \div 10,000
106
×
37
÷
10
,
000
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x
×
y
=
3
x \times y = 3
x
×
y
=
3
and
x
+
y
=
5
x + y = 5
x
+
y
=
5
Find
x
x
x
and
y
y
y
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For the function
f
(
x
)
=
x
2
−
2
f(x)=x^{2}-2
f
(
x
)
=
x
2
−
2
, find the slope of the secant line between
x
=
−
5
x=-5
x
=
−
5
and
x
=
−
2
x=-2
x
=
−
2
.
\newline
Answer:
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write an equation of an exponential function that passes through the points
(
2
,
200
)
(2, 200)
(
2
,
200
)
and
(
−
1
,
102.4
)
(-1, 102.4)
(
−
1
,
102.4
)
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Let
x
3
+
y
2
=
24
x^{3}+y^{2}=24
x
3
+
y
2
=
24
.
\newline
What is the value of
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
at the point
(
2
,
4
)
(2,4)
(
2
,
4
)
?
\newline
Give an exact number.
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Complete the equation of the line through
(
−
8
,
−
2
)
(-8,-2)
(
−
8
,
−
2
)
and
(
−
4
,
6
)
(-4,6)
(
−
4
,
6
)
. Use exact numbers.
\newline
y
=
□
y=\square
y
=
□
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Complete the point-slope equation of the line through
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
and
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
Use exact numbers.
\newline
y
−
(
−
1
)
=
□
y-(-1)=\square
y
−
(
−
1
)
=
□
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Complete the point-slope equation of the line through
(
1
,
0
)
(1,0)
(
1
,
0
)
and
(
6
,
−
3
)
(6,-3)
(
6
,
−
3
)
.
\newline
Use exact numbers.
\newline
y
−
(
−
3
)
=
□
y-(-3)=\square
y
−
(
−
3
)
=
□
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Complete the point-slope equation of the line through
(
−
1
,
−
10
)
(-1,-10)
(
−
1
,
−
10
)
and
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
Use exact numbers.
\newline
y
−
2
=
y-2=
y
−
2
=
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Complete the point-slope equation of the line through
(
−
9
,
6
)
(-9,6)
(
−
9
,
6
)
and
(
−
7
,
−
8
)
(-7,-8)
(
−
7
,
−
8
)
.
\newline
Use exact numbers.
\newline
y
−
6
=
y-6=
y
−
6
=
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Complete the point-slope equation of the line through
(
−
8
,
−
8
)
(-8,-8)
(
−
8
,
−
8
)
and
(
−
7
,
9
)
(-7,9)
(
−
7
,
9
)
. Use exact numbers.
\newline
y
−
9
=
y-9=
y
−
9
=
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Complete the point-slope equation of the line through
(
3
,
6
)
(3,6)
(
3
,
6
)
and
(
5
,
−
8
)
(5,-8)
(
5
,
−
8
)
. Use exact numbers.
\newline
y
−
6
=
y-6=
y
−
6
=
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Complete the point-slope equation of the line through
(
−
8
,
−
1
)
(-8,-1)
(
−
8
,
−
1
)
and
(
−
6
,
5
)
(-6,5)
(
−
6
,
5
)
. Use exact numbers.
\newline
y
−
5
=
y-5=
y
−
5
=
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