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?
Signup and view all the answers
If the x coordinate is positive and the y coordinate is positive, in which quadrant does the point lie?
Signup and view all the answers
Name a point in the 3rd quadrant.
Signup and view all the answers
What is the x-intercept of $5x - 8y = 14$?
Signup and view all the answers
What is the x-intercept of $g(x) = 3x - 15$?
Signup and view all the answers
What is the y-intercept of $y = 6x - 12$?
Signup and view all the answers
What is the y-intercept of $4 - 2y = 3x$?
Signup and view all the answers
What is the slope of the equation $6x - 3y = 27$?
Signup and view all the answers
What is the rate of change between the points (5,3) and (-4,2)?
Signup and view all the answers
What is the rate of change between the points (7, -3) and (7, 4)?
Signup and view all the answers
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?
Signup and view all the answers
Any diagonal line is all...?
Signup and view all the answers
Any horizontal line is all...?
Signup and view all the answers
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 =.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
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.
