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Chapter 12: Problem 51

Are the graphs of \(y=3 x-8\) and \(y=-3 x+8\) perpendicular?

Short Answer

Expert verified
No, the lines are not perpendicular.

Step by step solution

01

Determine the slope of the first line

The equation of the first line is \(y = 3x - 8\). The coefficient of \(x\) is the slope of the line. So, for the first line, the slope \(m_1 = 3\)
02

Determine the slope of the second line

The equation of the second line is \(y = -3x + 8\). The coefficient of \(x\) is the slope of the line. So, for the second line, the slope \(m_2 = -3\)
03

Check if the product of the slopes equals -1

The product of \(m_1\) and \(m_2\) is \(3 \times -3 = -9\). As this does not equal -1, the lines are not perpendicular.

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Most popular questions from this chapter

A graphing calculator can be used to graph a linear equation. Here are the keystrokes to graph \(y=\frac{2}{3} x+1 .\) First the equation is entered. Then the domain (Xmin to Xmax) and the range (Ymin to Ymax) are entered. This is called the viewing window. Xmin and Xmax are the smallest and largest values of \(x\) that will be shown on the screen. Ymin and Ymax are the smallest and largest values of \(y\) that will be shown on the screen. Use a graphing calculator to graph the equation. $$y=2 x+1$$ For \(2 x,\) you may enter \(2 \times x\) or just \(2 x\). Entering the times sign \(\times\) is not necessary on many graphing calculators.

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Determine whether there is a line that contains all of the given points. If so, find the equation of the line. $$(-1,-5),(2,4),(0,2)$$
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