chap1-summary.xml

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<section xml:id="chap1-summary" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Chapter Summary and Review</title>
<subsection><title>Key Concepts</title>
<p>
	<ol label="*1*">
		<li><p>We can describe a relationship between variables with a table of values, a graph, or an equation.</p></li>
		<li><p>Linear models have equations of the following form:
			<me>y = (\text{starting value}) + (\text{rate of change}) \cdot x</me>
		</p></li>
		<li><p>The general form for a linear equation is <m>Ax + By = C</m>.</p></li>
		<li><p>We can use the <term>intercepts</term> to graph a line. The intercepts are also useful for interpreting a model.</p></li>
		<li><p>A <term>function</term> is a rule that assigns to each value of the input variable a unique value of the output variable.</p></li>
		<li><p>Function notation: <m>y = f (x)</m>, where <m>x</m> is the input and <m>y</m> is the output.</p></li>
		<li><p>The point <m>(a, b)</m> lies on the graph of the function <m>f</m> if and only if <m>f (a) = b</m></p></li>
		<li><p>Each point on the graph of the function <m>f</m> has coordinates <m>(x, f (x))</m> for some value of <m>x</m>.</p></li>
		<li><p>The <term>vertical line test</term> tells us whether a graph represents a function.</p></li>
		<li><p>Lines have constant slope.</p></li>
		<li><p>The slope of a line gives us the <term>rate of change</term> of one variable with respect to another</p></li>
		<li><p>
			<assemblage><title>Formulas for Linear Functions</title><p>
                \begin{align*}
                \text{Slope:}<ampersand /> <ampersand />m <ampersand />=\dfrac{\Delta y}{\Delta x}
                = \dfrac{y_2 -y_1}{x_2 -x_1}<backslash /><backslash />
                <ampersand /><ampersand /><ampersand /> = \dfrac{f(x_2) - f(x_1)}{x_2 -x_1}<backslash /><backslash />
                \text{Slope-intercept form:}<ampersand /> <ampersand />y <ampersand />=b + mx<backslash /><backslash />
                \text{Point-slope form:}<ampersand /> <ampersand />y <ampersand />=y_1 + m(x - x_1)
                \end{align*}
			</p></assemblage>
		</p></li>
		<li><p>The <term>slope-intercept form</term> is useful when we know the initial value and the rate of change.</p></li>
		<li><p>The <term>point-slope form</term> is useful when we know the rate of change and one point on the line.</p></li>
		<li><p>Linear functions form a <term>two-parameter family</term>, <m>f (x) = b + mx</m>.</p></li>
		<li><p>We can approximate a linear pattern by a <term>regression line</term>.</p></li>
		<li><p>We can use <term>interpolation</term> or <term>extrapolation</term> to make estimates and predictions.</p></li>
		<li><p>If we extrapolate too far beyond the known data, we may get unreasonable results.</p></li>
	</ol>.
</p>
</subsection>
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</section>
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