Algebra2Ch1cont pt.13

Service Description

'Linear Inequalities in Two Variables' "Graphing an 'inequality' (< <_, >, >_) is different from graphing an 'equation' (=). The 'solution' to an inequality is 'half a plane', or all the points on one side of the line, indicated graphically by shading. The points on the line are included if the symbol is >_ or <_. This represented by drawing a solid line. The points on the line are excluded if the symbol is < or >. This is represented by drawing a dashed line. To sketch an inequality follow these steps: 1. Graph the line (solve for y and then use the slope-intercept method or a table). Sketch a dashed line (< or >) or a solid line (<_ or>_) depending on the inequality "symbol'. Label the equation on the line. 2. Shade the appropriate 'half plane. a. shade up (y> or y >_) or shade down (y < or y<_) from a horizontal or diagonal line. b. Shade right (x> or x>_) or shade left (x< or x<_) from a vertical line. Some people like to check their shading by testing a particular point. Pick a point that is 'not' on the line (the origin is as easy choice as long as it is not on the line) and check it in the original inequality ( the equation). If the inequality is true for that point, then the half plane that includes that point, then the half plane that includes that point should be shaded, If the selected point does not check in the inequality, then the half plane not containing that point should be shaded". (kicking it out of the group) Example 1.23 Sketch the graph of 3x -2y< -4. Solution First solve for y 3x -2y< -4 -2y< -3 -4 y>3x/2 +2 Notice how the inequality sign changed direction because you divided by -2. Now graph the line. Draw a dashed line because of the strict inequality. Then shade the appropriate half plane, in this case above the line because of the > symbol. (Now Grandma's head has been working on this. If there were a section of cubes or a painted square and one could mark the x and y lines on it with something your fingers could feel and something else with a different feel could be placed or you could place it with a spot of two on the y line and the slope showing on the run of three steps up and two steps over that will show in the not or shaded area. Grandma found it from the x line as 2 over and 3 up.) You can confirm the shading is correct by checking the coordinates of the origin in the inequality: 3(0) - 2(0) < -4 is false, so the half plane should be shaded (with a cloth).