Explanation Given: y = 7 x − 4 ; ( 2 , ) , ( − 1 , ) , ( 0 , ) Approach Used: The rectangular coordinate system consists of two number lines intersecting at the point 0 on each number line. The horizontal number line is called the x -axis and the vertical number line is called the y -axis. Every point in the rectangular coordinate system corresponds to an ordered pair of numbers such as Thus, to find if an ordered pair is a solution of an equation, i. Replaced the variables by the coordinates of the ordered pair. ii. Solve. iii. If the equation is a true statement then the given ordered pair is a solution of the given equation. A linear equation in two variables is an equation that can be written in the form a x + b y = c where a , b , and c are numbers, a and b are not both 0 . To graph a linear equation in two variables, follow the steps below:- i. If the equation is of form y = a where a is a number, then the graph of y = a is a horizontal line that crosses the y -axis at a and parallel to the x -axis. Else proceed to next step. ii. If the equation is of form x = a where a is a number, then the graph of x = a is a vertical line that crosses the x -axis at a and parallel to the y -axis. Else proceed to next step. iii. Find three ordered pair solutions of the given equation by assuming the x -value or y -value and replacing the x -value or y -value in the given equation. iv. Plot these three ordered pair solutions on the graph. To graph a point, its position is first located on the x -axis, then on the y -axis and the point is finally plotted when this meet. Each ordered pair corresponds to one point in the graph. v. Draw a line through the plotted points. This the graph of the given linear equation. Calculation: Since, the given equation is not of form y = a or x = a . Hence, it is not parallel to x -axis or y -axis. Since, the given ordered pair is a solution of the given equation, it must satisfy the given equation. That is, replacing the variables in the given equation y = 7 x − 4 by the coordinates of the ordered pair ( 2 , ) , we get y = 7 ( 2 ) − 4 y = 14 − 4 y = 10 Thus, the first ordered pair solution for the given equation is ( 2 , 10 )

7th Edition

ISBN: 9780321955043

Author: Elayn Martin-Gay

Publisher: PEARSON

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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The given ordered pair solutions of each equation and graph it.

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The given ordered pair solutions of each equation and graph it.

Solution Summary: The author explains how the rectangular coordinate system consists of two number lines intersecting at the point 0 on each number line.

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To complete: The given ordered pair solutions of each equation and graph it.

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To complete:

The given ordered pair solutions of each equation and graph it.