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StephenElston
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Module01/01-02-Linear Equations.ipynb

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"metadata": {},
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"### Slope-Intercept Form\n",
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"One of the great things about algebraic expressions is that you can write the same equation in multiple ways, or *forms*. The *slope-intercept form* is a specific way of writing a 2-variable linear equation so that the equation definition includes the slope and y-intercept. The generalised slope-intercept form looks like this:\n",
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"One of the great things about algebraic expressions is that you can write the same equation in multiple ways, or *forms*. The *slope-intercept form* is a specific way of writing a 2-variable linear equation so that the equation definition includes the slope and y-intercept. The generalized slope-intercept form looks like this:\n",
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"\n",
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"\\begin{equation}y = mx + b \\end{equation}\n",
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"\n",
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"\n",
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"\\begin{equation}y = 1\\frac{1}{2}x + -2 \\end{equation}\n",
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"\n",
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"You can see intuitively that this is true. In our original form of the equation, to find y we multiply x by three, subtract 4, and divide by two - in other words, x is half of 3x - 4; which is 1.5x - 2. So these equations are equivalent, but the slope-intercept form has the advantages of being simpler, and including two key pieces of information we need to plot the line represented by the equation. We know the y-intecept that the line passes through (0, -2), and we know the slope of the line (for every x, we add 1.5 to y.\n",
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"You can see intuitively that this is true. In our original form of the equation, to find y we multiply x by three, subtract 4, and divide by two - in other words, x is half of 3x - 4; which is 1.5x - 2. So these equations are equivalent, but the slope-intercept form has the advantages of being simpler, and including two key pieces of information we need to plot the line represented by the equation. We know the y-intercept that the line passes through (0, -2), and we know the slope of the line (for every x, we add 1.5 to y.\n",
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"\n",
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"Let's recreate our set of test x and y values using the slope-intercept form of the equation, and plot them to prove that this describes the same line:"
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"mimetype": "text/x-r-source",
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"name": "R",
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"pygments_lexer": "r",
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"version": "3.4.1"
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"version": "3.5.0"
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}
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},
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"nbformat": 4,

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