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Chapter 3: Problem 52

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-4,2)\) and perpendicular to the line whose equation is \(y=\frac{1}{3} x+7\)

Short Answer

Expert verified
The equation of the line is \(y - 2 = -3(x + 4)\) in point-slope form and \(y = -3x - 10\) in slope-intercept form.

Step by step solution

01

Identify the slope of the given line

The slope of the given line \(y = \frac{1}{3}x + 7\) is \(\frac{1}{3}\), identified by extracting the coefficient of \(x\).
02

Find the slope of the perpendicular line

The slope of the line perpendicular to the given line is the negative reciprocal of the slope of given line. Hence, the slope of the required line is \(-1/\frac{1}{3} = -3\).
03

Write the equation of the line in point-slope form

Employing the coordinates of the given point \((-4,2)\) and the perpendicular slope \(-3\), the point-slope form of the line is : \(y - 2 = -3(x + 4)\).
04

Convert equation to slope-intercept form

To convert to slope-intercept form, which is \(y = mx + c\), simplify the point-slope equation: \(y = -3x - 10\).

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Most popular questions from this chapter

Use a graphing utility to graph each equation in Exercises in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1] .\) Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{1}{2} x$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line is perpendicular to the line whose equation is \(4 x-y=6\) and has the same \(y\) -intercept as this line.

Explain how to graph a linear equation of the form \(A x+B y=0\).

Will help you prepare for the material covered in the next section. Solve for \(y: 2 x+5 y=0\)

Use intercepts to graph \(3 x-5 y=15\) (Section \(3.2,\) Example 4 )
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