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Questions and Answers
What is the maximum power of a variable in a linear equation?
What is the maximum power of a variable in a linear equation?
Which of the following equations is a linear equation?
Which of the following equations is a linear equation?
What are the coordinates of the origin in rectangular coordinates?
What are the coordinates of the origin in rectangular coordinates?
If the slope of a line is described as undefined, which of the following can be true?
If the slope of a line is described as undefined, which of the following can be true?
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How is the slope of a line calculated between two points (x1, y1) and (x2, y2)?
How is the slope of a line calculated between two points (x1, y1) and (x2, y2)?
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What does the x-intercept of a line represent?
What does the x-intercept of a line represent?
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What is the y-intercept of a linear equation?
What is the y-intercept of a linear equation?
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In which quadrant is the point (3, 5) located?
In which quadrant is the point (3, 5) located?
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Which equation represents the general form of a linear equation?
Which equation represents the general form of a linear equation?
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What are the values of A, B, and C for the equation 4x - 2y = 8?
What are the values of A, B, and C for the equation 4x - 2y = 8?
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In point-slope form, which variable represents the slope of the line?
In point-slope form, which variable represents the slope of the line?
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For the equation y = 3x + 5, what is the y-intercept?
For the equation y = 3x + 5, what is the y-intercept?
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What does the point (x1, y1) represent in the point-slope form equation?
What does the point (x1, y1) represent in the point-slope form equation?
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To find the x-intercept of a linear equation, which value must y be set to?
To find the x-intercept of a linear equation, which value must y be set to?
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Which form of a linear equation uses the slope and the y-intercept?
Which form of a linear equation uses the slope and the y-intercept?
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What is the general form of the equation for a vertical line?
What is the general form of the equation for a vertical line?
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What is the first step when using the method of substitution to solve a system of linear equations?
What is the first step when using the method of substitution to solve a system of linear equations?
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Why might the method of elimination be preferred over substitution?
Why might the method of elimination be preferred over substitution?
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What does it mean when two linear equations have the same slope?
What does it mean when two linear equations have the same slope?
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In the context of linear equations, what scenario represents coincident lines?
In the context of linear equations, what scenario represents coincident lines?
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What is the purpose of back-substitution in the method of substitution?
What is the purpose of back-substitution in the method of substitution?
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What happens when you take the sum of two equations in a system?
What happens when you take the sum of two equations in a system?
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What results from solving the equation $2x - y = 8$ for y?
What results from solving the equation $2x - y = 8$ for y?
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What is a key characteristic of intersecting lines in a pair of linear equations?
What is a key characteristic of intersecting lines in a pair of linear equations?
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What is the slope of the line that passes through the points (2,5) and (-2,13)?
What is the slope of the line that passes through the points (2,5) and (-2,13)?
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Which of the following equations represents a line perpendicular to L: $2x + 3y = 6$?
Which of the following equations represents a line perpendicular to L: $2x + 3y = 6$?
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What is the y-intercept of the line represented by the equation $3x + 4y = 20$?
What is the y-intercept of the line represented by the equation $3x + 4y = 20$?
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Given the line $x - 4y = 8$, what is the equation of a line parallel to it that passes through the point (2, 1)?
Given the line $x - 4y = 8$, what is the equation of a line parallel to it that passes through the point (2, 1)?
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What are the x and y intercepts of the line $4x - 3y = 24$?
What are the x and y intercepts of the line $4x - 3y = 24$?
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Which of the following lines is parallel to the x-axis?
Which of the following lines is parallel to the x-axis?
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If point P(2,5) lies on the line $kx + 3y + 9 = 0$, what is the value of k?
If point P(2,5) lies on the line $kx + 3y + 9 = 0$, what is the value of k?
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Which of the following points form lines that are parallel to each other?
Which of the following points form lines that are parallel to each other?
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What is the equation of the line that passes through the point (0, 5) and is vertical?
What is the equation of the line that passes through the point (0, 5) and is vertical?
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What is the equation of a horizontal line that passes through the point (-4, -3)?
What is the equation of a horizontal line that passes through the point (-4, -3)?
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To find the intersection of the lines x + y = 5 and 3x - y = 7, what would you need to solve?
To find the intersection of the lines x + y = 5 and 3x - y = 7, what would you need to solve?
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If a line passes through the points (-5, -4) and is parallel to another line passing through (-3, 2) and (6, 8), what can be concluded about their slopes?
If a line passes through the points (-5, -4) and is parallel to another line passing through (-3, 2) and (6, 8), what can be concluded about their slopes?
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What is the slope of a line that is parallel to the line represented by the equation 2x - y + 2 = 0?
What is the slope of a line that is parallel to the line represented by the equation 2x - y + 2 = 0?
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What slope must a line have to be parallel to a line with a slope of 4?
What slope must a line have to be parallel to a line with a slope of 4?
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If a student has a loan of $8250 and pays $125 a month, what is the expression for the remaining amount, P, in terms of t?
If a student has a loan of $8250 and pays $125 a month, what is the expression for the remaining amount, P, in terms of t?
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How many tickets were sold if a concert brought in RM432500 from 9500 tickets sold at both RM35 and RM55?
How many tickets were sold if a concert brought in RM432500 from 9500 tickets sold at both RM35 and RM55?
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Study Notes
Linear Equations
- A linear equation represents a straight line.
- The highest power of any variable in a linear equation is 1.
- Linear equations can have one or more variables.
Rectangular Coordinates
- The horizontal axis is the x-axis.
- The vertical axis is the y-axis.
- The point where the x and y axes intersect is the origin (0,0).
- The axes divide the plane into four quadrants (numbered counterclockwise).
Slope of a Line
- Slope (m) measures the steepness of a line.
- The formula for calculating slope is: m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are two points on the line.
- A horizontal line has a slope of 0.
- A vertical line has an undefined slope.
Intercepts of a Line
- The x-intercept is the point where the line crosses the x-axis (y = 0).
- The y-intercept is the point where the line crosses the y-axis (x = 0).
Forms of Linear Equations
- General Form: Ax + By = C, where A, B, and C are constants, and x and y are variables. A and B cannot both be zero.
- Point-Slope Form: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
- Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
Graphing Linear Equations
- To graph a linear equation, find the intercepts (x-intercept and y-intercept) and plot them on the coordinate plane.
- Connect the plotted points to form a straight line.
Solving Systems of Linear Equations
- Substitution Method: Solve one equation for one variable, and substitute that expression into the other equation to solve for the remaining variable.
- Elimination Method: Manipulate the equations (multiplying or adding) to eliminate one variable and solve for the other.
Pairs of Linear Equations
- Coincident: The lines overlap completely.
- Parallel: The lines never intersect.
- Intersecting: The lines cross at a single point.
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Description
This quiz covers the fundamentals of linear equations, including their components, slope calculations, intercepts, and coordinate systems. Test your knowledge of how to represent and analyze linear equations using rectangular coordinates and their various forms.
