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Chapter 1: Problem 32

Find an equation of the line that passes through the given points. $$ (2,1) \text { and }(2,5) $$

Short Answer

Expert verified
The equation of the line passing through the points \((2,1)\) and \((2,5)\) is \(x=2\).

Step by step solution

01

Finding the equation of a vertical line

To find the equation of the vertical line that passes through the points (2, 1) and (2, 5), observe that the x-coordinate is the same for both points which is 2. The equation of a vertical line passing through a point with x-coordinate (a) is given by: x = a
02

Writing the equation of the line

Since the x-coordinate of both points is 2, the equation of the vertical line that passes through them is: x = 2

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Most popular questions from this chapter

Find an equation of the line that satisfies the given condition. $$ \text { The line parallel to the } x \text { -axis and } 6 \text { units below it } $$

Determine whether the points lie on a straight line. $$ A(-2,1), B(1,7), \text { and } C(4,13) $$

The relationship between the temperature in degrees Fahrenheit \(\left({ }^{\circ} \mathrm{F}\right)\) and the temperature in degrees Celsius \(\left({ }^{\circ} \mathrm{C}\right)\) is $$ F=\frac{9}{5} C+32 $$ a. Sketch the line with the given equation. b. What is the slope of the line? What does it represent? c. What is the \(F\) -intercept of the line? What does it represent?

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept }-\frac{1}{2} ; y \text { -intercept } \frac{3}{4} $$

Moody's Corporation is the holding company for Moody's Investors Service, which has a \(40 \%\) share in the world credit-rating market. According to Company Reports, the total revenue (in billions of dollars) of the company is projected to be as follows \((x=0\) correspond to 2004\()\) : $$ \begin{array}{lccccc} \hline \text { Year } & 2004 & 2005 & 2006 & 2007 & 2008 \\ \hline \text { Revenue, } \boldsymbol{y} & 1.42 & 1.73 & 1.98 & 2.32 & 2.65 \\\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the results of part (a) to estimate the rate of change of the revenue of the company for the period in question. c. Use the result of part (a) to estimate the total revenue of the company in 2010 , assuming that the trend continues.
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