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Chapter 0: Problem 13

Sketching Lines In Exercises 13 and \(14,\) sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes. \(\begin{array}{ll}{\text { Point }} & {\text { Slopes }} \\ {(3,4)} & {\text { (a) } 1} & {\text { (b) }-2 \quad \text { (c) }-\frac{3}{2} \quad \text { (d) Undefined }}\end{array}\)

Short Answer

Expert verified
The solution will be a graph with four lines passing through the point (3,4). The lines have the slopes of 1, -2, -3/2 and undefined respectively.

Step by step solution

01

Plotting a Line With Slope 1

Locate the point (3,4) on the graph. Since the slope is 1, for every step along the x-axis (right if positive, left if negative), step the same amount up or down on the y-axis. Draw the line through these points.
02

Plotting a Line With Slope -2

Again start from the point (3,4) on the graph. Because the slope is -2, for every step along the positive x-axis, we move 2 steps downwards on the y-axis. Similarly, for every step along the negative x-axis, move 2 steps upwards on the y-axis. Draw the line through these points.
03

Plotting a Line With Slope -3/2

From the point (3,4), this time the slope is -3/2. That means, for every 2 steps along the positive x-axis, move 3 steps down on the y-axis. Conversely, for every 2 steps along the negative x-axis, move 3 steps up on the y-axis. Draw the line through these points.
04

Plotting a Line With Undefined Slope

When the slope is undefined, the line is vertical. Plot a line through the point (3,4) that goes straight up and down.

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Most popular questions from this chapter

Deciding Whether an Equation Is a Function In Exercises \(43-46,\) determine whether \(y\) is a function of \(x\). $$x^{2}+y=16$$

Combinations of Functions In Exercises 59 and 60, find (a) \(f(x)+g(x),\) (b) \(f(x)-g(x)\)(c) \(f(x) \cdot g(x),\) and (d) \(f(x) / g(x)\) $$\begin{array}{l}{f(x)=x^{2}+5 x+4} \\ {g(x)=x+1}\end{array}$$

Modeling Data An instructor gives regular 20 -point quizzes and 100 -point exams in a mathematics course. Average scores for six students, given as ordered pairs \((x, y),\) where \(x\) is the average quiz score and \(y\) is the average exam score, are \((18,87),(10,55),(19,96),(16,79),(13,76),\) and \((15,82) .\) (a) Use the regression capabilities of a graphing utility to find the least squares regression line for the data. (b) Use a graphing utility to plot the points and graph the regression line in the same viewing window. (c) Use the regression line to predict the average exam score for a student with an average quiz score of \(17 .\) (d) Interpret the meaning of the slope of the regression line. (e) The instructor adds 4 points to the average exam score of everyone in the class. Describe the changes in the positions of the plotted points and the change in the equation of the line.

If \(f(x)=f(-x)\) for all \(x\) in the domain of \(f,\) then the graph of \(f\) is symmetric with respect to the \(y\) -axis.

\(\begin{array}{l}{\text { Writing Use a graphing utility to graph the polynomial }} \\ {\text { functions }} \\\ {p_{1}(x)=x^{3}-x+1 \text { and } p_{2}(x)=x^{3}-x} \\ {\text { How many zeros does each function have? Is there a cubic }} \\ {\text { polynomial that has no zeros? Explain. }}\end{array}\)
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