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Chapter 3: Problem 213

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form. . line \(x=7\), point (-3,-4)

Short Answer

Expert verified
y = -4

Step by step solution

01

Identify the Slope of the Given Line

The given line is a vertical line, represented by the equation \(x = 7\). Vertical lines have an undefined slope.
02

Determine the Slope of the Perpendicular Line

A line perpendicular to a vertical line is a horizontal line. Horizontal lines have a slope of \(0\).
03

Write the Equation of the Line

For a horizontal line passing through a point (\(x_1, y_1\)), the equation is \(y = y_1\). Since the line passes through the point (-3, -4), the equation is \(y = -4\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope-intercept form
The slope-intercept form is a common way to write the equation of a line. The general formula is \(y = mx + b\), where:
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