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Math Problems
Grade 8
Write a linear equation from two points
Complete the equation of the line through
(
−
8
,
8
)
(-8,8)
(
−
8
,
8
)
and
(
1
,
−
10
)
(1,-10)
(
1
,
−
10
)
. Use exact numbers.
\newline
y
=
□
+
x
‾
‾
‾
y=\square \underline{+\underline{\underline{x}}}
y
=
□
+
x
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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.
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Complete the point-slope equation of the line through
(
−
4
,
8
)
(-4, 8)
(
−
4
,
8
)
and
(
4
,
4
)
(4, 4)
(
4
,
4
)
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A line passes through the points
(
−
2
,
−
16
)
(-2, -16)
(
−
2
,
−
16
)
and
(
4
,
20
)
(4 ,20)
(
4
,
20
)
. Write its equation in slope-intercept form.
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A line passes through the points
(
1
,
1
)
(1,1)
(
1
,
1
)
and
(
2
,
8
)
(2,8)
(
2
,
8
)
. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
−
1
,
10
)
(-1,10)
(
−
1
,
10
)
and
(
4
,
−
10
)
(4,-10)
(
4
,
−
10
)
. Write its equation in slope-intercept form.
\newline
Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
−
1
,
−
9
)
(-1,-9)
(
−
1
,
−
9
)
and
(
1
,
7
)
(1,7)
(
1
,
7
)
. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
1
,
1
)
(1,1)
(
1
,
1
)
and
(
2
,
7
)
(2,7)
(
2
,
7
)
. Write its equation in slope-intercept form.
\newline
Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
−
1
,
−
7
)
(-1,-7)
(
−
1
,
−
7
)
and
(
7
,
1
)
(7,1)
(
7
,
1
)
. Write its equation in slope-intercept form.
\newline
Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
−
2
,
−
3
)
(-2,-3)
(
−
2
,
−
3
)
and
(
1
,
−
9
)
(1,-9)
(
1
,
−
9
)
. Write its equation in slope-intercept form.
\newline
Write your answer using integers, proper fractions, and improper fractions in simplest form.
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A line passes through the points
(
−
1
,
−
8
)
(-1,-8)
(
−
1
,
−
8
)
and
(
1
,
6
)
(1,6)
(
1
,
6
)
. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
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Two integers have a sum of
−
1
-1
−
1
and a product of
−
56
-56
−
56
. What is the positive difference between the two integers?
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A line passes through the points
(
−
3
,
−
4
)
(-3, -4)
(
−
3
,
−
4
)
and
(
6
,
−
10
)
(6, -10)
(
6
,
−
10
)
. Write its equation in slope-intercept form.
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\begin{aligned} y&=10+16x-x^2 \\ y&=3x+50 \end{aligned} If
(
x
1
,
y
1
)
(x_1,y_1)
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
(x_2,y_2)
(
x
2
,
y
2
)
are distinct solutions to the system of equations shown, what is the sum of the
y
1
y_1
y
1
and
y
2
y_2
y
2
?
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What is the slope of a line that passes through the points
(
1
,
3
)
(1,3)
(
1
,
3
)
and
(
7
,
5
)
(7,5)
(
7
,
5
)
in the
x
y
x y
x
y
-plane?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
\frac{1}{3}
3
1
\newline
(B)
2
2
2
\newline
(C)
3
3
3
\newline
(D)
6
6
6
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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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Complete the equation of the line through
(
2
,
1
)
(2,1)
(
2
,
1
)
and
(
5
,
−
8
)
(5,-8)
(
5
,
−
8
)
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Complete the equation of the line through
(
−
10
,
3
)
(-10,3)
(
−
10
,
3
)
and
(
−
8
,
−
8
)
(-8,-8)
(
−
8
,
−
8
)
Get tutor help
Complete the equation of the line through
(
3
,
−
8
)
(3,-8)
(
3
,
−
8
)
and
(
6
,
−
4
)
(6,-4)
(
6
,
−
4
)
Get tutor help
Complete the equation of the line through
(
−
10
,
−
7
)
(-10,-7)
(
−
10
,
−
7
)
and
(
−
5
,
−
9
)
(-5,-9)
(
−
5
,
−
9
)
Get tutor help
Complete the point-slope equation of the line through
(
−
4
,
8
)
(-4,8)
(
−
4
,
8
)
and
(
4
,
4
)
(4,4)
(
4
,
4
)
. Use exact numbers.
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
9
)
(0,9)
(
0
,
9
)
and
(
4
,
144
)
(4,144)
(
4
,
144
)
.
\newline
Answer:
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
4
)
(0,4)
(
0
,
4
)
and
(
5
,
128
)
(5,128)
(
5
,
128
)
.
\newline
Answer:
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
16
)
(0,16)
(
0
,
16
)
and
(
2
,
784
)
(2,784)
(
2
,
784
)
.
\newline
Answer:
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
3
)
(0,3)
(
0
,
3
)
and
(
4
,
1875
)
(4,1875)
(
4
,
1875
)
.
\newline
Answer:
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
9
)
(0,9)
(
0
,
9
)
and
(
2
,
324
)
(2,324)
(
2
,
324
)
.
\newline
Answer:
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Write the equation of the line that passes through the points
(
2
,
−
4
)
(2,-4)
(
2
,
−
4
)
and
(
−
1
,
−
5
)
(-1,-5)
(
−
1
,
−
5
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
1
,
9
)
(1,9)
(
1
,
9
)
and
(
−
3
,
2
)
(-3,2)
(
−
3
,
2
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
−
6
,
−
1
)
(-6,-1)
(
−
6
,
−
1
)
and
(
8
,
4
)
(8,4)
(
8
,
4
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
−
5
,
9
)
(-5,9)
(
−
5
,
9
)
and
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
−
6
,
6
)
(-6,6)
(
−
6
,
6
)
and
(
0
,
9
)
(0,9)
(
0
,
9
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
5
,
9
)
(5,9)
(
5
,
9
)
and
(
−
2
,
−
8
)
(-2,-8)
(
−
2
,
−
8
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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Write the equation of the line that passes through the points
(
−
3
,
8
)
(-3,8)
(
−
3
,
8
)
and
(
3
,
2
)
(3,2)
(
3
,
2
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
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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
Get tutor help
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:
Get tutor help
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:
Get tutor help
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
)
Get tutor help
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
=
□
Get tutor help
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
=
Get tutor help
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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