Algebra 1 Practice Quiz
This is a quiz covering topics from the first semester of Algebra 1.
- 1.
The ordered pair (3,0) is found:
- A.
On the y-axis
- B.
In the first Quadrant
- C.
In the fourth Quadrant
- D.
On the x-axis
Correct Answer
D. On the x-axisExplanation
The ordered pair (3,0) is found on the x-axis because the x-coordinate is 3 and the y-coordinate is 0. The x-axis is the horizontal line where the y-coordinate is always 0. Therefore, the point (3,0) lies on the x-axis.Rate this question:
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- 2.
(-3, 7) is located in quadrant:
- A.
I
- B.
II
- C.
III
- D.
IV
Correct Answer
B. IIExplanation
The point (-3, 7) is located in quadrant II because the x-coordinate (-3) is negative and the y-coordinate (7) is positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive.Rate this question:
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- 3.
The price of a house increased by 7%. If the new price is $107,000, what was the original cost of the house?
- A.
$100,000
- B.
$114,490
- C.
$99,510
- D.
$93,000
Correct Answer
A. $100,000Explanation
The original cost of the house was $100,000. This can be determined by dividing the new price of $107,000 by 1.07, which represents a 7% increase. The result is $100,000, which is the original cost of the house.Rate this question:
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- 4.
(8,2) is a solution of x - 3y = 6
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The point (8,2) is not a solution of the equation x - 3y = 6 because when we substitute x = 8 and y = 2 into the equation, we get 8 - 3(2) = 8 - 6 = 2, which is not equal to 6. Therefore, the statement is false.Rate this question:
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- 5.
The graph of y = 2x + 3 passes through the origin.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The graph of y = 2x + 3 does not pass through the origin because when x = 0, y = 3. Therefore, the statement is false.Rate this question:
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- 6.
What is the y- intercept for 5y = 4x - 20?
- A.
(5,0)
- B.
(0,5)
- C.
(-4,0)
- D.
(0,-4)
Correct Answer
C. (-4,0)Explanation
To find the y-intercept, we first set the value of x to 0 in the equation. This eliminates the x-term, leaving us with an equation only involving y. We then solve for y to determine the y-coordinate where the graph intersects the y-axis, representing the y-intercept. In this case, when x is 0, y is calculated to be -4. Therefore, the y-intercept is the point (0, -4).Rate this question:
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- 7.
What quadrant does the line 5x + 3y = 15 not pass through?
- A.
I
- B.
II
- C.
III
- D.
IV
Correct Answer
C. IIIExplanation
The line 5x + 3y = 15 does not pass through quadrant III. This is because in quadrant III, both x and y values are negative. Plugging in negative values for x and y into the equation would result in a sum greater than 15, making it impossible for the line to pass through quadrant III.Rate this question:
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- 8.
What is the x-intercept of x =2?
- A.
(0,2)
- B.
(2,0)
- C.
(0,0)
- D.
There is no x-intercept
Correct Answer
D. There is no x-interceptExplanation
The equation x = 2 represents a vertical line passing through the point (2,0) on the x-axis. Since this line is parallel to the y-axis, it does not intersect the x-axis at any point. Therefore, there is no x-intercept for the given equation.Rate this question:
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- 9.
What is the slope of the line through (6,5) and (9,1)?
- A.
4/3
- B.
-3/4
- C.
-4/3
- D.
3/4
Correct Answer
C. -4/3Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (6,5) and (9,1). Plugging these values into the formula, we get (1 - 5) / (9 - 6) = -4 / 3. Therefore, the slope of the line is -4/3.Rate this question:
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- 10.
What is the slope of the line x = 7?
- A.
7
- B.
0
- C.
1/7
- D.
Undefined
Correct Answer
D. UndefinedExplanation
The slope of a line is defined as the change in the y-coordinates divided by the change in the x-coordinates. In the given equation x = 7, the value of x is always 7, meaning that there is no change in the x-coordinate. Therefore, the change in the y-coordinate is also undefined, resulting in an undefined slope.Rate this question:
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- 11.
Find the slope of the line 6x-2y=12-2y?
- A.
6
- B.
1/6
- C.
0
- D.
Undefined
Correct Answer
D. UndefinedExplanation
The given equation is in the form 6x - 2y = 12 - 2y. By simplifying the equation, we can see that the variable "y" cancels out on both sides, resulting in 6x = 12. Since there is no "y" term in the equation, the slope of the line is undefined.Rate this question:
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- 12.
Find an equation for the line with slope and y-intercept 3.
- A.
4x - 3y = -3
- B.
4x - 3y = -9
- C.
3y - 4x = -3
- D.
3y - 4x = -9
Correct Answer
B. 4x - 3y = -9Explanation
The equation 4x - 3y = -9 represents the line with a slope of 4 and a y-intercept of 3. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, when we rearrange the equation, we get y = (4/3)x + 3, which matches the slope and y-intercept given in the question. Therefore, 4x - 3y = -9 is the correct equation for the line.Rate this question:
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- 13.
Find an equation of the line through (25) with a slope of .
- A.
Y - x = 4
- B.
2y - 3x = 4
- C.
3x - 2y = 4
- D.
X - y = 4
Correct Answer
B. 2y - 3x = 4Explanation
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where:
m is the slope of the line
(x1, y1) is a point on the line
In this case, we have m = 3/2 and (x1, y1) = (2, 5). Substituting these values into the point-slope form, we get:
y - 5 = (3/2)(x - 2)
Multiplying both sides by 2 to eliminate the fraction, we get:
2y - 10 = 3x - 6
Rearranging the terms, we get the equation in standard form:
2y - 3x = 4Rate this question:
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- 14.
Find an equation of a line through (3,4) and (1,-7).
- A.
11x - 2y = -5
- B.
11x - 2y = -1
- C.
2x - 11y = -38
- D.
11x - 2y = 25
Correct Answer
D. 11x - 2y = 25Explanation
To find the equation of a line, we need to determine its slope and y-intercept.
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1) m = (-7 - 4) / (1 - 3) m = -11 / -2 m = 11/2
Use the point-slope form:
y - y1 = m(x - x1) y - 4 = (11/2)(x - 3)
Simplify to slope-intercept form (y = mx + b):
y - 4 = (11/2)x - 33/2 y = (11/2)x - 33/2 + 4 y = (11/2)x - 25/2
Convert to standard form (Ax + By = C):
-11/2x + y = -25/2 11x - 2y = 25Rate this question:
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- 15.
Find an equation of a line through (0,2) parallel to the line 3x-6y=1.
- A.
2y - x = 4
- B.
2y x = 2x
- C.
Y - 2x = 2
- D.
Y - 2x = 4
Correct Answer
A. 2y - x = 4Explanation
The equation of a line parallel to 3x-6y=1 can be found by keeping the same slope. The slope of the given line is 3/6 or 1/2. Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the given point (0,2) to find the equation. Therefore, the equation of the line parallel to 3x-6y=1 and passing through (0,2) is 2y - x = 4.Rate this question:
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Sep 30, 2024Quiz Edited by
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Mar 28, 2011Quiz Created by
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