Podcast
Questions and Answers
What is the slope of the line represented by the equation 2x - y = 4?
What is the slope of the line represented by the equation 2x - y = 4?
The line represented by the equation 2x - y = 4 intersects the y-axis at the point (0, -4).
The line represented by the equation 2x - y = 4 intersects the y-axis at the point (0, -4).
True (A)
What is the x-intercept of the line represented by the equation 2x - y = 4?
What is the x-intercept of the line represented by the equation 2x - y = 4?
(2, 0)
The equation 2x - y = 4 can be written in slope-intercept form as ______.
The equation 2x - y = 4 can be written in slope-intercept form as ______.
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Match the following forms of the equation with their descriptions:
Match the following forms of the equation with their descriptions:
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Which of the following points lies on the line represented by the equation 2x - y = 4?
Which of the following points lies on the line represented by the equation 2x - y = 4?
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The equation 2x - y = 4 represents a parabola.
The equation 2x - y = 4 represents a parabola.
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If the value of x is -1, what is the corresponding value of y in the equation 2x - y = 4?
If the value of x is -1, what is the corresponding value of y in the equation 2x - y = 4?
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Flashcards
Linear Equation
Linear Equation
An equation that represents a straight line in a coordinate system.
Slope-Intercept Form
Slope-Intercept Form
The form of a linear equation written as y = mx + b.
Slope
Slope
The steepness of a line; calculated as 'rise/run'.
Y-Intercept
Y-Intercept
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Graphing a Line
Graphing a Line
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Standard Form
Standard Form
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Infinitely Many Solutions
Infinitely Many Solutions
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Applications of Linear Equations
Applications of Linear Equations
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Study Notes
Equation Analysis
- The given equation is a linear equation in two variables, x and y.
- It represents a straight line on a Cartesian coordinate system.
- The equation can be written in the form (y = 2x - 4). This is the slope-intercept form, where the slope is 2 and the y-intercept is -4.
Graphing the Equation
- To graph the line, start by plotting the y-intercept at (0, -4).
- Use the slope (2, which can be expressed as rise/run = 2/1) to find another point. From the y-intercept, move one unit to the right (run=1), and two units up (rise=2). This gives you the point (1, -2).
- To verify, substitute x = 1 and y = -2 into the original equation, which yields 2(1) - (-2) = 4, validating the point.
- Continue this process to plot more points and sketch the line.
Solving for x and y
- Given a value for x, you can solve for y in the equation y = 2x - 4.
- Given a value for y, you can solve for x in the equation x = (y+4)/2.
- There are infinitely many solutions to the equation as there are infinite points on the line, each corresponding to a unique value of x and y.
- Example solutions:
- If x = 2, then y = 2(2) - 4 = 0, giving the point (2, 0).
- If x = 0, then y = 2(0) - 4 = -4, giving the point (0, -4).
- If y = 2, then 2 = 2x - 4, so 2x = 6, and x = 3, giving the point (3, 2).
Slope-Intercept Form
- The equation can be expressed in slope-intercept form: (y = mx + b), where:
- m is the slope of the line, representing the rate of change of y with respect to x.
- b is the y-intercept, the point where the line intersects the y-axis.
Standard Form
- The equation can also be written in standard form: (Ax + By = C), where A, B, and C are integers. In this case, (2x - y = 4) is already in standard form.
Solutions and Points
- Every point on the line determined by the equation 2x - y = 4 represents a solution to the equation.
Applications
- The equation 2x - y = 4 has applications in various fields:
- Physics: Modelling linear relationships between quantities.
- Economics: Representing supply and demand.
- Engineering: Describing linear patterns.
- Mathematics: General use.
Important Considerations
- The equation is linear, resulting in a straight-line graph.
- It defines a single straight line with an infinite number of points satisfying the equation.
- The equation shows a relationship between x and y, displaying how a change in x affects y and vice versa.
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Description
This quiz covers the fundamentals of linear equations, specifically analyzing and graphing the equation in slope-intercept form. You'll learn how to plot points on a Cartesian coordinate system and solve for variables within the equation. Test your understanding of the concepts and practice solving linear equations.
