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What Do All Lines y=ax+a Have in Common?

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Introduction to Linear Polynomials · Chapter challenge problems · 3:30

You'll learn: Factor a(x+1) and discover common graphical features.

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What Do All Lines y=ax+a Have in Common?

3:30

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What Do All Lines y=ax+a Have in Common?

You'll learn: Factor a(x+1) and discover common graphical features.

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Same topic

Chapter challenge problems

8

Reverse the Digits and Find the Number
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Reverse the Digits and Find the Number
You'll learn: Use place value and two digit conditions to recover a two-digit number.
Rearrange an Equation Before Reading Its Slope
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Rearrange an Equation Before Reading Its Slope
You'll learn: Rewrite equations in y=ax+b, graph them and identify parallel pairs.
Convert Between Kelvin and Fahrenheit
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Convert Between Kelvin and Fahrenheit
You'll learn: Use a linear temperature formula forwards and backwards.
Work Done as a Linear Graph
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Work Done as a Linear Graph
You'll learn: Express work as force times distance and interpret the graph.
Recover a Linear Polynomial from Two Points
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Recover a Linear Polynomial from Two Points
You'll learn: Find a and b from two graph points, then locate both axis crossings.
Find Two Polynomials from Their Sum and a Graph Condition
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Find Two Polynomials from Their Sum and a Graph Condition
You'll learn: Combine p(0), a zero of p−q and the sum identity to recover both rules.
Count Matchsticks in a Growing Chain of Hexagons
3:25
Count Matchsticks in a Growing Chain of Hexagons
You'll learn: Derive a stage rule using shared sides and test whether a total is possible.
Find a Parallel Line from a Single Point
3:29
Find a Parallel Line from a Single Point
You'll learn: Find one linear rule from two points, then use its slope to recover a parallel rule.

Next topic

Counting and the origins of numbers

5

Counting Before Numerals: Match One Object to Another
3:26
Counting Before Numerals: Match One Object to Another
You'll learn: Explain one-to-one correspondence and why counting numbers were needed.
Tally Marks, Grouping and the History of Counting
3:36
Tally Marks, Grouping and the History of Counting
You'll learn: Explore the chapter’s bone-tally examples and the need for larger-number notation.
Trade Ratios and Prime-Number Groups
3:26
Trade Ratios and Prime-Number Groups
You'll learn: Apply counting to a trade ratio and identify the property of a numerical group.
Why Counting Numbers Are Not Enough for Subtraction
3:22
Why Counting Numbers Are Not Enough for Subtraction
You'll learn: Test closure under addition and subtraction and motivate larger number systems.
Count to Twelve on One Hand
3:30
Count to Twelve on One Hand
You'll learn: Explain the finger-joint counting method and its connection with base twelve.

Next topic

Zero and integers

2

Zero as a Placeholder and as a Number
3:35
Zero as a Placeholder and as a Number
You'll learn: Distinguish an empty place in numeral notation from zero as a quantity used in arithmetic.
What Happens When We Calculate with Zero?
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What Happens When We Calculate with Zero?
You'll learn: Explain a−a=0, a+0=a, a−0=a and a×0=0.