Lesson 4-6 Pages 177-181

Functions and Linear Equations

What you will learn!

How to graph linear equations.

FunctionFunctionFunction tableFunction tableDomainDomainRangeRangeLinear equationLinear equation

What you really need to know!The solution of an equation with two variables consists of two numbers, one for each variable, that make the equation true. The solution is usually written as an ordered pair (x, y), which can be graphed.

What you really need to know!

If the graph for an equation is a straight line, then the equation is a linear equation.

Example 1:

Ann makes $6.00 an hour working at a grocery store. Make a function table that shows Ann’s total earnings for working 1, 2, 3, and 4 hours.

To solve this problem, we are going to make a table with:

Input, Instructions, and Output.InputInput InstructionsInstructions OutputOutput

Example 1:

InputInput Function RuleFunction Rule OutputOutput

Number of Number of hourshours Multiply by 6Multiply by 6 Total Total

Earnings ($)Earnings ($)

11 1 x 61 x 6 6622 2 x 62 x 6 121233 3 x 63 x 6 181844 4 x 64 x 6 2424

Domain Range

Ann makes $6.00 an hour working at a grocery store. Make a function table that shows Ann’s total earnings for working 1, 2, 3, and 4 hours.

Example 2:

Graph y = x + 3xx x + 3x + 3 yy (x, y)(x, y)22 2 + 32 + 3 55 (2, 5)(2, 5)11 1 + 31 + 3 44 (1, 4)(1, 4)00 0 + 30 + 3 33 (0, 3)(0, 3)-1-1 -1 + 3-1 + 3 22 (-1, 2)(-1, 2)

(x, y)(x, y)(2, 5)(2, 5)(1, 4)(1, 4)(0, 3)(0, 3)(-1, 2)(-1, 2)

Example 3:

Graph y = x – 3xx x – 3x – 3 yy (x, y)(x, y)22 2 – 32 – 3 -1-1 (2, -1)(2, -1)11 1 – 31 – 3 -2-2 (1, -2)(1, -2)00 0 – 30 – 3 -3-3 (0, -3)(0, -3)-1-1 -1 – 3-1 – 3 -4-4 (-1, -4)(-1, -4)

(x, y)(x, y)(2, -1)(2, -1)(1, -2)(1, -2)(0, -3)(0, -3)(-1, -4)(-1, -4)

Example 4:

Graph y = -3xxx -3x-3x yy (x, y)(x, y)22 -3-3•2•2 -6-6 (2, -6)(2, -6)11 -3-3•1•1 -3-3 (1, -3)(1, -3)00 -3-3•0•0 00 (0, 0)(0, 0)-1-1 -3-3•-1•-1 33 (-1, 3)(-1, 3)

(x, y)(x, y)(2, -6)(2, -6)(1, -3)(1, -3)(0, 0)(0, 0)(-1, 3)(-1, 3)

Example 5:

Graph y = -3x + 2xx -3x + 2-3x + 2 yy (x, y)(x, y)22 -3-3•2 + 2•2 + 2 -4-4 (2, -4)(2, -4)11 -3-3•1 + 2•1 + 2 -1-1 (1, -1)(1, -1)00 -3-3•0 + 2•0 + 2 22 (0, 2)(0, 2)-1-1 -3-3•-1 + 2•-1 + 2 55 (-1, 5)(-1, 5)

(x, y)(x, y)(2, -4)(2, -4)(1, -1)(1, -1)(0, 2)(0, 2)(-1, 5)(-1, 5)

Example 6:

Blue whales can reach a speed of 30 miles per hour in burst when in danger. The equation d = 30t describes the distance d that a whale traveling at that speed can travel in time t. Represent the function with a graph.

tt 30t30t dd (t, d)(t, d)11 30 30 1 1 3030 (1, 30)(1, 30)

22 30 30 2 2 6060 (2, 60)(2, 60)

33 30 30 3 3 9090 (3, 90)(3, 90)

44 30 30 4 4 120120 (4, 120)(4, 120)

d = 30t

Blue whales can reach a speed of 30 miles per hour in burst when in danger. The equation d = 30t describes the distance d that a whale traveling at that speed can travel in time t. Represent the function with a graph.

(t, d)(t, d)(1, 30)(1, 30)

(2, 60)(2, 60)

(3, 90)(3, 90)

(4, 120)(4, 120)

(5, 150)(5, 150)

(6, 180)(6, 180)

60

120

180

240

300

360

02 4 860

Page 179

Guided Practice

#’s 3-7

1 - 2 -12 - 2 03 - 2 14 - 2 2

4•-1 -44•0 04•1 44•2 8

Pages 177-179 with someone at home and study

examples!

Read:

Homework: Page 180-181

#’s 8-20 even

#’s 47-56

Lesson Check 4-6

1 - 4 -32 - 4 -23 - 4 -14 - 4 0

1 + 5 62 + 5 73 + 5 84 + 5 9

2•-1 -22•0 02•1 22•2 4

-6•-1 6-6•0 0-6•1 -6-6•2 -12

2•1-1 12•2-1 32•3-1 52•4-1 7

-2•-1- 2 0-2•0 - 2 -2-2•1 - 2 -4-2•2 - 2 -6

Page

573

Lesson 4-6

Lesson Check 4-6