Chapter 7: Problem 61
What is the graph of \(x=0\) ? What is the graph of \(y=0\) ? Explain your answers.
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Chapter 7: Problem 61
What is the graph of \(x=0\) ? What is the graph of \(y=0\) ? Explain your answers.
These are the key concepts you need to understand to accurately answer the question.
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Contains the point \((1,3)\) and is parallel to the line \(x+5 y=9\)
Contains the point \((2,-4)\) and is parallel to the \(y\) axis
$$ \begin{array}{ll|llll} 2 x-y=6 & \mathbf{x} & -2 & 0 & 2 & 4 \\ \hline \mathbf{y} & & & & \end{array} $$
Graph \(|x-y|>2\).
Now let's use a graphing calculator to get a graph of \(\mathrm{C}=\frac{5}{9}(\mathrm{~F}-32)\). By letting \(\mathrm{F}=x\) and \(\mathrm{C}=y\), we obtain Figure 7.15. Pay special attention to the boundaries on \(x\). These values were chosen so that the fraction \(\frac{\text { (Maximum value of } x \text { ) minus (Minimum value of } x \text { ) }}{95}\) would be equal to 1 . The viewing window of the graphing calculator used to produce Figure \(7.15\) is 95 pixels (dots) wide. Therefore, we use 95 as the denominator of the fraction. We chose the boundaries for \(y\) to make sure that the cursor would be visible on the screen when we looked for certain values. \(7.2\) = Linear Inequalities in Two Variables 337 Now let's use the TRACE feature of the graphing calculator to complete the following table. Note that the cursor moves in increments of 1 as we trace along the graph. \begin{tabular}{l|lllllllll} \(\mathbf{F}\) & \(-5\) & 5 & 9 & 11 & 12 & 20 & 30 & 45 & 60 \\ \hline \(\mathbf{C}\) & & & & & & & & & \end{tabular} (This was accomplished by setting the aforementioned fraction equal to 1.) By moving the cursor to each of the F values, we can complete the table as follows. \begin{tabular}{r|rrrrrrrrr} \(\mathbf{F}\) & \(-5\) & 5 & 9 & 11 & 12 & 20 & 30 & 45 & 60 \\ \hline \(\mathbf{C}\) & \(-21\) & \(-15\) & \(-13\) & \(-12\) & \(-11\) & \(-7\) & \(-1\) & 7 & 16 \end{tabular} The \(C\) values are expressed to the nearest degree. Use your calculator and check the values in the table by using the equation \(\mathrm{C}=\frac{5}{9}(\mathrm{~F}-32)\).
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