1. Linear Inequalities B. Davis B. Davis MathScience Innovation Center

2. Linear Inequalities B. Davis MathScience Innovation Center We started studying functions… 1 st : we defined relations 1 st : we defined relations 2 nd : we specified which relations are functions using lists, mappings, and graphs 2 nd : we specified which relations are functions using lists, mappings, and graphs 3 rd : we looked at special functions: 3 rd : we looked at special functions:  one-to-one  constant  linear

3. Linear Inequalities B. Davis MathScience Innovation Center Straight lines - all 4 kinds vertical : are relations, not functions vertical : are relations, not functions horizontal: special linear functions called “constant” where m = 0. horizontal: special linear functions called “constant” where m = 0. diagonal: linear with positive or negative slope diagonal: linear with positive or negative slope All linear functions have the form All linear functions have the form y=mx + b where m is__________ and b is ________________ y=mx + b where m is__________ and b is ________________ slope y-intercept

4. Linear Inequalities B. Davis MathScience Innovation Center The Linear Family of Functions Any function with x raised to the first power is related to the Linear Family Any function with x raised to the first power is related to the Linear Family y = m x + b y = m x + b y = |x| or y = abs ( x ) y = |x| or y = abs ( x ) y = [ x ] or y = int (x) y = [ x ] or y = int (x) y > mx + b y > mx + b y < mx + b y < mx + b Linear Equation Absolute Value Function Greatest Integer Function Linear Inequality

5. Linear Inequalities B. Davis MathScience Innovation Center Which are linear functions ? 1. y =5 x – 9 2. y 2 – 5 = 8x 3. y = 5/x 4. 5x + y = 19 5. y = 1 and 4 only

6. Linear Inequalities B. Davis MathScience Innovation Center Linear Inequalities are not functions but they are bordered by linear functions but they are bordered by linear functions For linear inequalities in 2 variables, a dotted line is to a _______________ of a linear inequality in 1 variable. For linear inequalities in 2 variables, a dotted line is to a _______________ of a linear inequality in 1 variable. For linear inequalities in 2 variables, a solid line is to a _______________ of a linear inequality in 1 variable. For linear inequalities in 2 variables, a solid line is to a _______________ of a linear inequality in 1 variable. open dot closed dot

7. Linear Inequalities B. Davis MathScience Innovation Center y > 2 x + 3 use a dotted line to draw y = 2x +3 use a dotted line to draw y = 2x +3 then shade above the line, since y > then shade above the line, since y > use a test point to be sure! use a test point to be sure! on the calculator use y = on the calculator use y =

8. Linear Inequalities B. Davis MathScience Innovation Center y < 2 x + 3 use a solid line to draw y = 2x +3 use a solid line to draw y = 2x +3 then shade below the line, since y < then shade below the line, since y < use a test point to be sure! use a test point to be sure! on the calculator use y = on the calculator use y =