Podcast
Questions and Answers
What is the slope of the line represented by the equation $y = -2x$?
What is the slope of the line represented by the equation $y = -2x$?
The slope of a horizontal line is always greater than zero.
The slope of a horizontal line is always greater than zero.
False
What type of line is represented by the slope of the points (-4, 5) and (6, 5)?
What type of line is represented by the slope of the points (-4, 5) and (6, 5)?
horizontal
The slope of the line represented by the equation $y = 2x - 3$ is ___.
The slope of the line represented by the equation $y = 2x - 3$ is ___.
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Match the equations with their corresponding descriptions:
Match the equations with their corresponding descriptions:
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Between Train A and Train B, which train travels faster based on the equations provided?
Between Train A and Train B, which train travels faster based on the equations provided?
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Study Notes
Graphing Linear Equations
- Graphing a linear equation can be done by plotting points and drawing a line through them:
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y = -2x
- For x = 0, y = 0
- For x = 1, y = -2
- For x = -1, y = 2
-
y = 2x - 3
- For x = 0, y = -3
- For x = 1, y = -1
- For x = -1, y = -5
-
y = -2x
Slope of Linear Equations
- The slope of a vertical line is undefined
- The slope of a horizontal line is 0
- The slope of a line can be calculated using two points on the line: (y2 - y1) / (x2 - x1)
- The line through the points (-4, 5) and (6, 5) has a slope of 0 because the y-values are the same, making the line horizontal.
Interpreting Linear Equations in Real-World Scenarios
- The profit (y in dollars) for a business from selling x coats is represented by y = 51x. This means that for every coat sold, the profit increases by $51.
- Train A travels at 76 miles per hour, represented by y = 76x. Train B travels at 64 miles per hour, as shown in the graph. Therefore, Train B is faster.
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Description
This quiz covers key concepts in graphing linear equations, including plotting points, understanding slopes, and interpreting equations in real-world scenarios. You'll learn how to calculate slopes and graph lines from given equations, important for mastering algebraic functions.
