Questions and Answers
Name 2 solutions of the equation $5x - 3y = 12$.
(3,1) (6,6)
Name 2 solutions of the equation $6y - 18 = 3x$.
(2,4) (4,5)
How many solutions does the equation $f(x) = 4x - 7$ have?
Infinitely many
What is the point (0,0) called?
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If the x coordinate is positive and the y coordinate is positive, in which quadrant does the point lie?
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Name a point in the 3rd quadrant.
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What is the x-intercept of $5x - 8y = 14$?
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What is the x-intercept of $g(x) = 3x - 15$?
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What is the y-intercept of $y = 6x - 12$?
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What is the y-intercept of $4 - 2y = 3x$?
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What is the slope of the equation $6x - 3y = 27$?
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What is the rate of change between the points (5,3) and (-4,2)?
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What is the rate of change between the points (7, -3) and (7, 4)?
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On Jose's 3rd birthday he weighed 34.2 pounds. Today on his 8th birthday he weighs 54.4 pounds. What is the yearly average rate of change of Jose's weight?
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Any diagonal line is all...?
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Any horizontal line is all...?
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Study Notes
Solutions of Equations
- The equation 5x - 3y = 12 has solutions (3, 1) and (6, 6).
- The equation 6y - 18 = 3x has solutions (2, 4) and (4, 5).
Nature of Solutions
- The equation f(x) = 4x - 7 has infinitely many solutions.
Coordinate System
- The point (0, 0) is referred to as the Origin.
- Points with positive x and y coordinates lie in the 1st Quadrant.
- Points in the 3rd Quadrant have negative x and y coordinates.
Intercepts
- The x-intercept of the equation 5x - 8y = 14 is (14/5, 0).
- The x-intercept of g(x) = 3x - 15 is (5, 0).
- The y-intercept of y = 6x - 12 is (0, -12).
- The y-intercept of 4 - 2y = 3x is (0, 2).
Slope and Rate of Change
- The slope of the equation 6x - 3y = 27 is 2.
- The rate of change between the points (5, 3) and (-4, 2) is 1/9.
- The rate of change between the points (7, -3) and (7, 4) is Undefined.
Average Rate of Change
- Jose's yearly average rate of change in weight from age 3 to age 8 is 4.04 pounds/year.
Characteristics of Lines
- Any diagonal line represents all real numbers.
- Any horizontal line also represents all real numbers in the form y =.
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Test your understanding of key concepts from Algebra 1 Unit 3 with these flashcards. Covering equations, their solutions, and important terminology, this quiz is designed to help you prepare for your final exam. Perfect for reinforcing your knowledge in algebraic fundamentals.