Linear Inequalities
B. DavisB. Davis
MathScience Innovation CenterMathScience Innovation Center
Linear Inequalities B. Davis MathScience Innovation Center
We started studying functions…
11stst: we defined relations: we defined relations 22ndnd: we specified which relations are : we specified which relations are
functions using lists, mappings, and graphsfunctions using lists, mappings, and graphs 33rdrd: we looked at special functions:: we looked at special functions:
one-to-oneone-to-one constantconstant linearlinear
Linear Inequalities B. Davis MathScience Innovation Center
Straight lines - all 4 kinds
vertical : are relations, not functionsvertical : are relations, not functions horizontal: special linear functions called horizontal: special linear functions called
“constant” where m = 0.“constant” where m = 0. diagonal: linear with positive or negative diagonal: linear with positive or negative
slopeslope All All linear functionslinear functions have the form have the form y=mx + b where m is__________ and b is y=mx + b where m is__________ and b is
________________________________slopeslope
y-intercepty-intercept
Linear Inequalities B. Davis MathScience Innovation Center
The Linear Family of Functions
Any function with x raised to the first Any function with x raised to the first power is related to the power is related to the Linear FamilyLinear Family
y = m x + by = 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 + by > mx + b yy < < mx + b mx + b
Linear Equation
Absolute Value Function
Greatest Integer Function
Linear Inequality
Linear Inequalities B. Davis MathScience Innovation Center
Which are linear functions ?
1.1. y =5 x – 9y =5 x – 9
2.2. yy22 – 5 = 8x – 5 = 8x
3.3. y = 5/xy = 5/x
4.4. 5x + y = 195x + y = 19
5.5. y = y =
1 and 4 only
3x
Linear Inequalities B. Davis MathScience Innovation Center
Linear Inequalities are not functions but they are bordered by linear functionsbut they are bordered by linear functions For linear inequalities in 2 variables, a For linear inequalities in 2 variables, a
dotted line is to a _______________ of a dotted line is to a _______________ of a linear inequality in 1 variable.linear inequality in 1 variable.
For linear inequalities in 2 variables, a solid For linear inequalities in 2 variables, a solid line is to a _______________ of a linear line is to a _______________ of a linear inequality in 1 variable.inequality in 1 variable.
open dotopen dot
closed dotclosed dot
Linear Inequalities B. Davis MathScience Innovation Center
y > 2 x + 3 use a dotted line to draw y = 2x +3use 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 =
6
4
2
-2
-4
-5 5 10
f x = 2x+3
Linear Inequalities B. Davis MathScience Innovation Center
y < 2 x + 3 use a solid line to draw y = 2x +3use 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 =
6
4
2
-2
-4
-5 5 10
f x = 2x+3
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