Linear Equations

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6 Terms

1
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Equations

statements that two expressions are equal

2
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Linear Equations

equations in which each variable is raised to the power of 1 (not higher) and without products of variables

3
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Equivalent

two equations that have the same solution

4
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The Number Line

geometric approach

the number line representation for numbers: ℝ

<p>geometric approach</p><p>the number line representation for numbers: ℝ</p>
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The Cartesian Plane

2D generalization of the number line: ℝ2

  • horizontal axis: 𝑥-axis

  • vertical axis: 𝑦-axis

  • each point is an ordered pairs of numbers: Point (𝑥, 𝑦)

  • Point (0, 0): the origin of the Cartesian plane

<p><span>2D generalization of the number line: ℝ<sup>2</sup></span></p><ul><li><p><span>horizontal axis: </span><span style="font-family: &quot;Cambria Math&quot;">𝑥</span><span>-axis</span></p></li><li><p><span>vertical axis: </span><span style="font-family: &quot;Cambria Math&quot;">𝑦</span><span>-axis</span></p></li><li><p><span>each point is an ordered pairs of numbers: Point (</span><span style="font-family: &quot;Cambria Math&quot;">𝑥</span><span>, </span><span style="font-family: &quot;Cambria Math&quot;">𝑦</span><span>)</span></p></li><li><p><span>Point (0, 0): the origin of the Cartesian plane</span></p></li></ul><p></p>
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3D Space

A generalization of the 2D Cartesian plane: ℝ3

three orthogonal axes: x, y and 𝑧

each point is an ordered 3 tuple of numbers: Point (x, y, z)

Point (0, 0, 0): the origin of the 3D

<p><span>A generalization of the 2D Cartesian plane: </span><span style="font-family: &quot;Cambria Math&quot;">ℝ</span><span><sup>3</sup></span></p><p><span>three orthogonal axes: x, y and 𝑧</span></p><p>each point is an ordered 3 tuple of numbers: Point (x, y, z)</p><p>Point (0, 0, 0): the origin of the 3D</p>

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