Q. Which of the following statements is true about the equation 4x - 5y = 20?
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A.
It represents a vertical line.
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B.
It has a positive slope.
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C.
It has no x-intercept.
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D.
It is a horizontal line.
Solution
Rearranging the equation to slope-intercept form gives y = (4/5)x - 4, indicating a positive slope.
Correct Answer:
B
— It has a positive slope.
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Q. Which of the following statements is true about the linear equation 4x - 5y = 20?
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A.
It has no solutions.
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B.
It has infinitely many solutions.
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C.
It has exactly one solution.
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D.
It is a quadratic equation.
Solution
A linear equation in two variables has exactly one solution unless it is a special case (like parallel lines). Here, it is a standard linear equation.
Correct Answer:
C
— It has exactly one solution.
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Q. Which of the following statements is true regarding the graph of a linear equation?
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A.
It can be a curve.
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B.
It is always a straight line.
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C.
It can have multiple slopes.
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D.
It can intersect the x-axis at multiple points.
Solution
The graph of a linear equation is always a straight line.
Correct Answer:
B
— It is always a straight line.
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Q. Which of the following statements is true regarding the graph of the equation 3x + 4y = 12? (2023)
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A.
It intersects the x-axis at (4, 0).
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B.
It intersects the y-axis at (0, 3).
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C.
It has a positive slope.
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D.
It is a vertical line.
Solution
Setting y = 0 gives x = 4, indicating that the graph intersects the x-axis at (4, 0).
Correct Answer:
A
— It intersects the x-axis at (4, 0).
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Q. Which of the following statements is true regarding the graph of the equation 5x + 2y = 10?
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A.
It is a vertical line.
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B.
It is a horizontal line.
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C.
It has a positive slope.
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D.
It has a negative slope.
Solution
Rearranging the equation to y = -5/2x + 5 shows that the slope is negative.
Correct Answer:
D
— It has a negative slope.
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Q. Which of the following statements is true regarding the graph of the equation y = 2x + 1?
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A.
It is a vertical line.
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B.
It has a positive slope.
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C.
It intersects the y-axis at -1.
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D.
It has a negative slope.
Solution
The equation y = 2x + 1 has a positive slope of 2 and intersects the y-axis at 1.
Correct Answer:
B
— It has a positive slope.
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Q. Which of the following statements is true regarding the graph of the equation y = mx + b?
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A.
The graph is always a circle.
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B.
The slope m indicates the steepness of the line.
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C.
The y-intercept b is always negative.
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D.
The graph can never be horizontal.
Solution
In the equation y = mx + b, m represents the slope, which indicates how steep the line is.
Correct Answer:
B
— The slope m indicates the steepness of the line.
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Q. Which of the following statements is true regarding the solutions of the equation 5x + 2y = 10?
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A.
It has no solutions.
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B.
It has one solution.
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C.
It has infinitely many solutions.
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D.
It has two solutions.
Solution
This linear equation represents a line, which has infinitely many solutions.
Correct Answer:
B
— It has one solution.
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