Graphs of Linear Inequalities Quiz

PDF page 422: Just like maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. The rectangular coordinate system is also called the xy-plane or the ‘coordinate plane’. The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The x-axis and the y-axis together form the rectangular coordinate system. These axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See Figure 4.2.

PDF page 422: Just like maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. The rectangular coordinate system is also called the xy-plane or the ‘coordinate plane’. The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The x-axis and the y-axis together form the rectangular coordinate system. These axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See Figure 4.2.

PDF page 422: In the rectangular coordinate system, every point is represented by an ordered pair. The first number in the ordered pair is the x-coordinate of the point, and the second number is the y-coordinate of the point.

PDF page 422: The first number is the x-coordinate. The second number is the y-coordinate. The phrase ‘ordered pair’ means the order is important. What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is (0, 0) . The point (0, 0) has a special name. It is called the origin.

PDF page 422: The first number is the x-coordinate. The second number is the y-coordinate. The phrase ‘ordered pair’ means the order is important. What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is (0, 0) . The point (0, 0) has a special name. It is called the origin.

PDF page 422: The point (0, 0) is called the origin. It is the point where the x-axis and y-axis intersect.

PDF page 423: The first number of the coordinate pair is the x-coordinate, and the second number is the y-coordinate. a Since x = −5 , the point is to the left of the y-axis. Also, since y = 4 , the point is above the x-axis. The point (−5, 4) is in Quadrant II. b Since x = −3 , the point is to the left of the y-axis. Also, since y = −4 , the point is below the x-axis. The point (−3, −4) is in Quadrant III. c Since x = 2 , the point is to the right of the y-axis. Since y = −3 , the point is below the x-axis. The point (2, −3) is in Quadrant lV. d Since x = −2 , the point is to the left of the y-axis. Since y = 3 , the point is above the x-axis. The point (−2, 3) is in Quadrant II. 5 e Since x = 3 , the point is to the right of the y-axis. Since y = , the point is above the x-axis. (It may be 2 5 ⎛ 5⎞

PDF page 424: (x, y) (x, y) (x, y) (x, y) ( + , + ) (−, + ) (−, −) ( + , −)

PDF page 425: Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates (a, 0) . Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates (0, b) .

PDF page 427: An equation of the form Ax + By = C , where A and B are not both zero, is called a linear equation in two variables. Notice the word line in linear. Here is an example of a linear equation in two variables, x and y .

PDF page 428: By rewriting y = −3x + 5 as 3x + y = 5 , we can easily see that it is a linear equation in two variables because it is of the form Ax + By = C . When an equation is in the form Ax + By = C , we say it is in standard form.

PDF page 428: A linear equation is in standard form when it is written Ax + By = C .

PDF page 428: Most people prefer to have A , B , and C be integers and A ≥ 0 when writing a linear equation in standard form, although it is not strictly necessary. Linear equations have infinitely many solutions. For every number that is substituted for x there is a corresponding y value. This pair of values is a solution to the linear equation and is represented by the ordered pair (x, y) . When we substitute these values of x and y into the equation, the result is a true statement, because the value on the left side is equal to the value on the right side.

PDF page 430: We can find more solutions to the equation by substituting in any value of x or any value of y and solving the resulting equation to get another ordered pair that is a solution. There are infinitely many solutions of this equation.

PDF page 428: Most people prefer to have A , B , and C be integers and A ≥ 0 when writing a linear equation in standard form, although it is not strictly necessary. Linear equations have infinitely many solutions. For every number that is substituted for x there is a corresponding y value. This pair of values is a solution to the linear equation and is represented by the ordered pair (x, y) . When we substitute these values of x and y into the equation, the result is a true statement, because the value on the left side is equal to the value on the right side.

PDF page 428: An ordered pair (x, y) is a solution of the linear equation Ax + By = C , if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.

PDF page 428: An ordered pair (x, y) is a solution of the linear equation Ax + By = C , if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.