Pre-Algebra Demystified
CHAPTER 11 Graphing 209 Hence, (4, 2) is a solution to 3xy¼10. Math Note: The solution can be checked by substituting both valu ...
Graphing Lines Equations of the form axþby¼c where a, b, and c are real numbers are calledlinear equations in two variablesand t ...
EXAMPLE Draw the graph of 2xy¼8. SOLUTION Find the coordinates of two points on the line: Let x¼ 1 Let x¼ 5 2xy¼82xy¼ 8 2(1) ...
Math Note: When graphing lines, it is best to select three points rather than two points in case an error has been made. If an e ...
CHAPTER 11 Graphing 213 Fig. 11-10. Fig. 11-11. ...
214 CHAPTER 11 Graphing Fig. 11-12. Fig. 11-13. ...
Horizontal and Vertical Lines Any equation of the form x¼a, where a is a real number, is the graph of a vertical line passing th ...
PRACTICE Draw the graph of each of the following: y¼ 6 x¼ 4 y¼ 2 x¼ 3 y¼ 2 ANSWERS See Fig. 11-16 See Fig. 11-17 See Fig. 1 ...
CHAPTER 11 Graphing 217 Fig. 11-16. Fig. 11-17. ...
218 CHAPTER 11 Graphing Fig. 11-18. Fig. 11-19. ...
Intercepts The point on the graph where a line crosses the y axis is called they intercept (see Fig. 11-21). To find the y inter ...
EXAMPLE Find the y intercept of 2xþ3y¼9. SOLUTION Substitute 0 for x and solve for y: 2xþ3y¼ 9 2 ð 0 Þþ3y¼ 9 0 þ3y¼ 9 3y¼ 9 3y 3 ...
5xþ2y¼ 30 5xþ 2 ð 0 Þ¼ 30 5xþ 0 ¼ 30 5x¼ 30 5x 5 ¼ 30 5 x¼ 6 Hence, the x intercept is (6, 0). Math Note: It is easy to draw lin ...
On the graph of a line the slope can be found by selecting two points, forming a right triangle, and then counting the number of ...
CHAPTER 11 Graphing 223 SOLUTION Let x 1 ¼5, y 1 ¼ 3, and x 2 ¼8, y 2 ¼1, and then substitute in the slope formula: m¼ y 2 y 1 ...
Let x 1 ¼ 4 ;y 1 ¼5 and x 2 ¼2, y 2 ¼10. Now substitute in the slope formula: m¼ y 2 y 1 x 2 x 1 m¼ 10 ð 5 Þ 2 4 ¼ 15 ...
PRACTICE Find the slope of the line containing the two points (3, 4) and (6, 8). Find the slope of the line containing the two ...
SOLUTION Find two points on each line. For xþy¼8, use (7, 1) and (3, 5). For xy¼ 2, use (3, 1) and (6, 4). Graph both lines and ...
Math Note: To check, substitute the values of x and y for the solution in both equations and see if they are closed true equatio ...
2xþ3y¼ 12 xþ4y¼ 11 4xþy¼ 10 2xþy¼ 6 x5y¼ 6 5xy¼ 6 xþ3y¼ 7 6xy¼ 15 ANSWERS (7, 3) (3, 2) (2, 2) (1,1) (2,3) Quiz Use Fi ...
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