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Questions and Answers
Name 2 solutions of the equation $5x - 3y = 12$.
Name 2 solutions of the equation $5x - 3y = 12$.
(3,1) (6,6)
Name 2 solutions of the equation $6y - 18 = 3x$.
Name 2 solutions of the equation $6y - 18 = 3x$.
(2,4) (4,5)
How many solutions does the equation $f(x) = 4x - 7$ have?
How many solutions does the equation $f(x) = 4x - 7$ have?
Infinitely many
What is the point (0,0) called?
What is the point (0,0) called?
If the x coordinate is positive and the y coordinate is positive, in which quadrant does the point lie?
If the x coordinate is positive and the y coordinate is positive, in which quadrant does the point lie?
Name a point in the 3rd quadrant.
Name a point in the 3rd quadrant.
What is the x-intercept of $5x - 8y = 14$?
What is the x-intercept of $5x - 8y = 14$?
What is the x-intercept of $g(x) = 3x - 15$?
What is the x-intercept of $g(x) = 3x - 15$?
What is the y-intercept of $y = 6x - 12$?
What is the y-intercept of $y = 6x - 12$?
What is the y-intercept of $4 - 2y = 3x$?
What is the y-intercept of $4 - 2y = 3x$?
What is the slope of the equation $6x - 3y = 27$?
What is the slope of the equation $6x - 3y = 27$?
What is the rate of change between the points (5,3) and (-4,2)?
What is the rate of change between the points (5,3) and (-4,2)?
What is the rate of change between the points (7, -3) and (7, 4)?
What is the rate of change between the points (7, -3) and (7, 4)?
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?
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?
Any diagonal line is all...?
Any diagonal line is all...?
Any horizontal line is all...?
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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