Chapter 4 Graphing Linear Equations and Functions Algebra

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 1 – Plot Points in a Coordinate Plane – a plane formed by the intersection, also known as the origin, of a horizontal number line called the x-axis and a vertical number line called the y-axis. Quadrants – The four regions into which the coordinate plane is divided by the x-axis and the y-axis. Ordered Pair – a pair of numbers, the x-coordinate and y-coordinate, that can be used to locate a point on a coordinate plane. (x-coordinate, y-coordinate) Coordinate Plane

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 1 – Plot Points in a Coordinate Plane Example # 1 Using the Overhead, plot the points on the coordinate plane. Describe the location of each point. a) i) q) y) b) j) r) z) c) k) s) aa) d) l) t) ab) e) m) u) ac) f) n) v) ad) g) o) w) a) h) p) x) af)

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 1 – Plot Points in a Coordinate Plane Example # 2 Graph the function with the domain -4, -2, 0, 2, 4. Identify the range. Step 1: Make a Input-Output Table: x y = -(1/2)x +1 y -4 y = -(1/2)(-4) +1 3 -2 y = -(1/2)(-2) +1 2 0 y = -(1/2)(0) +1 1 2 y = -(1/2)(2) +1 0 4 y = -(1/2)(4) +1 -1 Step 3: Graph the Function, use the ordered pairs Step 2: List the Ordered Pairs: Step 4: Identify the range. -1, 0, 1, 2, 3.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Example # 3 Graph the equation 2 x + y = 2 Step 1 : Solve the given equation in terms of y. Step 4 : Connect the points by drawing a line with arrows at both ends. Step 2 : Make a Input-Output Table: x y = -2 x+2 Y -3 y =-2(-3)+2 8 -1 y =-2(-1)+2 4 0 y =-2(0)+2 2 1 y =-2(1)+2 0 3 y =-2(3)+2 -4 Step 3 : List & Plot the Ordered Pairs(Points)

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Standard Form of a Linear Equation – Ax + By = C where A, B, and C, are all real numbers A and B are not both zero. If either A or B is zero, then you have special types of lines. When A = 0, the equation becomes By = C or y = (C/B). Thus, y equals a constant value, or y = b. And that constant value forms a horizontal line. When B = 0, the equation becomes Ax = C or x = (C/A). Thus, x equals a constant value, or x = a. And that constant value forms a vertical line. HORIZONTAL AND VERTICAL LINES y=b In the coordinate plane, the graph y = b is a horizontal line. x=a In the coordinate plane, the graph x = a is a horizontal line.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Example # 4 Graph the equation y = -3 For every value of x, the value of y is -3. The graph of the equation, y = -3 is a horizontal line 3 units below the x-axis.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Example # 5 Graph the equation x = 2 For every value of y, the value of x is 2. The graph of the equation, x = 2, is a vertical line 2 units to the right of the y-axis.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Example # 6 Graph the function with the domain x ≤ 0. Identify the range of the function. Step 1: Make a Input-Output Table: Reminder: x must be less than 0 x y = (1/2)x -1 Step 3: Graph the Function, use the ordered pairs y 0 y = (1/2)(0) -1 -1 -2 y = (1/2)(-2) -1 -2 -4 y = (1/2)(-4) -1 -3 -6 y = (1/2)(-6) -1 -4 -8 y = (1/2)(-8) -1 -5 Step 2: List the Ordered Pairs: Step 4: Identify the range. y ≤ -1.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 22 Section 4. 2 – Graph Linear Equations Practice Problem Graph the function with the domain x ≤ 0. Identify the range of the function. Identify the range. y ≥ 1

Chapter 4 – Graphing Linear Equations and Functions Section 4. 1, 4. 2 Homework # 15 pg 209 # 3 – 21 odd; # 36 pg 219 # 3 – 21 mults. of 3; # 23 -29 all Algebra I A - Meeting 22