Questions and Answers
What is Standard Form?
Ax + By = C
What is Slope-Intercept Form?
y = mx + b
What is Point-Slope Form?
y - y1 = m(x - x1)
What is the formula for slope?
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What does the slope of zero look like on a graph and in fraction form?
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What does the slope of undefined look like on a graph and in fraction form?
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What does the graph look like for y = 1?
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What is the slope of the line x = -2?
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Write an equation with the given slope and y-intercept: slope = 2/7, y-intercept = -3.
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Write an equation with the given slope and y-intercept: slope = 0.8, y-intercept = 10.
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Write a linear equation in slope-intercept form to model the situation: A television repair shop charges $35 plus $20 per hour.
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Write a linear equation in slope-intercept form to model the situation: An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.
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Write a linear equation in slope-intercept form to model the situation: The temperature is 38 degrees and is expected to rise at a rate of 3 degrees per hour.
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Write a linear equation in slope-intercept form to model the situation: A taxi driver charges $5 plus $0.30 per mile.
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Find the inverse of the following set: {(1, 2), (3, -4), (-7, 9), (8, 8)}.
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Study Notes
Algebraic Forms and Definitions
- Standard Form: Equation of a line represented as Ax + By = C, where A, B, and C are integers.
- Slope-Intercept Form: Expresses the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.
- Point-Slope Form: Formulated as y - y1 = m(x - x1), allows calculation of the line's equation using a point (x1, y1) and slope m.
Slope Concepts
- Slope Formula: Calculated as m = (y2 - y1) / (x2 - x1), indicating the steepness of a line.
- Slope of Zero: Represents a horizontal line, mathematically expressed as 0/1.
- Undefined Slope: Represents a vertical line, mathematically expressed as 1/0.
Graphical Representations
- Horizontal Line Example: The equation y = 1 indicates every y value is 1, resulting in a horizontal line.
- Vertical Line Example: The equation x = 2 means every x value is -2, leading to a vertical line.
Writing Linear Equations
- To create an equation using slope and y-intercept:
- Slope: 2/7, y-intercept: -3 results in y = (2/7)x - 3.
- Slope: 0.8, y-intercept: 10 results in y = 0.8x + 10.
Real-World Situations Modeled as Linear Equations
- Television Repair Shop: Charges $35 plus $20 per hour modeled by y = 20x + 35.
- Melting Icicle: Starts at 12 inches, melts at 1/4 inch/hour, modeled by y = 12 - (1/4)x.
- Temperature Increase: Begins at 38 degrees, rises at 3 degrees/hour, resulting in y = 3x + 38.
- Taxi Fare: Charges $5 plus $0.30 per mile, modeled by y = 0.3x + 5.
Finding Inverses
- The inverse of the set {(1, 2), (3, -4), (-7, 9), (8, 8)} is found as {(2, 1), (-4, 3), (9, -7), (8, 8)}.
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Description
This quiz covers the key concepts of Algebra 1 Unit 5, focusing on different forms of linear equations such as Standard Form, Slope-Intercept Form, and Point-Slope Form. Test your understanding of slopes and their representations in various scenarios. Perfect for reviewing essential algebraic principles before exams.
