Line 1 is defined by \(y=3 x+7\), and line 2 is perpendicular to line 1. What is the slope of line 2 ? \(\bigcirc-3\) O \(\frac{1}{3}\) \(\bigcirc-\frac{1}{3}\) O I don't know.

Short Answer

Expert verified
The slope of line 2 is \(-\frac{1}{3}\).

Step by step solution

01

Find the slope of the given line

The general form of a line equation is \(y = mx + b\), where \(m\) is the slope. Here, line 1 is given by the equation \(y = 3x + 7\). So, the slope (m1) of line 1 is 3.
02

Determine the slope of a line perpendicular to line 1

The slope (m2) of a line that is perpendicular to line 1 is the negative reciprocal of m1. The negative reciprocal of a number is found by flipping the number and changing its sign. So, the slope of line 2 would be \(-\frac{1}{m1}\), which equals \(-\frac{1}{3}\).

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