Presentation on theme: "Linear Inequalities Page 178. Formulas of Lines Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + By."— Presentation transcript:
Formulas of Lines Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + By + C = 0 General Form a a a
Slopes of Parallel Lines Parallel lines have the same slope. If they are both in slope-intercept form then only the y-intercept is different. Examples y=2x+6y-3=4(x+1) y=2x-8y+2=4(x+9)
Slopes of Perpendicular Lines Perpendicular lines have slopes which are opposite reciprocals of each other. y=2x -2 is perpendicular to all lines y= -½ x + b for all values of b The product of the slopes of perpendicular lines is -1. 2 - ½ = -1
A linear inequality in 2 variables is a graph that is half of the coordinate plane. Draw the solid or dotted line and shade on one side of it. Linear Inequalities
< Is less than > is greater than ≥ is greater than or equal to ≤ is less than or equal to ≠ is not equal to or ≠ dotted line ≤ or ≥ solid line
A solution of an inequality in two variables, x and y, is an ordered pair of real numbers with the following property: When the coordinates are substituted into the inequality, we obtain a true statement. Every ordered pair that is part of the solution “satisfies” the inequality.
Determining if an ordered pair is a solution Substitute the ordered pair into both inequalities and see if the solutions are true. If both are true, the ordered pair is a solution. if the ordered pair gives a false solution in either equation, the ordered pair does not satisfy the system of inequalities. Is (3,1) a solution to the system of inequalities? y<2x-2 and y≥x-1
How to graph A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. 1)Graph it like an equation by plotting points and determine how to connect the points with a solid or dotted line. 2)Then determine where to shade!
Where do we shade?? If the equation is in slope intercept form with y on one side and everything else on the other, y> or y≥ shades above the line and y< and y≤ shade below the line. If you are not sure, pick a point not on the line and substitute it to see if it is a solution or not. If it is a solution shade there, if not, shade the other side.
A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. y>5x+2 noticed the dotted line
Graphing > or < graph with a dotted line ≥ or ≤ graph with a solid line Then determine where to shade. Pick a test point and if the inequality is true for the test point, graph that side of the line.