/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 If you know a point on a line an... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 35

If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation.

Short Answer

Expert verified
To find the equation of a line given a point on the line and the equation of a perpendicular line: (1) Identify the slope of the given line, (2) find the negative reciprocal of this slope to get the slope of the line we need, and (3) use the known point and the slope in the point-slope form of the line equation to get the required line's equation.

Step by step solution

01

Identify the Slope of the Perpendicular Line

First step is identifying the slope (m) of the given perpendicular line. If the equation is in the slope-intercept form (y = mx + b), the coefficient of x is the slope.
02

Calculate the Slope of the Line

Since the lines are perpendicular, the slope of the line we want to find is the negative reciprocal of the slope of the given perpendicular line. In other words, if the slope of the perpendicular line is \( a \), then the slope of the line will be \( -1/a \).
03

Write the Equation of the Line

Now we know the slope of the line and a point on it. Let's suppose that point is \((x_1, y_1)\) and the slope we calculated in Step 2 is \( b \). We can now use the point-slope form of a line equation, which is \( y - y_1 = b(x - x_1) \). Substitute \( x_1, y_1 \) and \( b \) into this equation to obtain the equation of the line.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+y^{2}=25$$

$$\text { Solve and check: } \frac{x-1}{5}-\frac{x+3}{2}=1-\frac{x}{4}$$

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-2)^{2}+(y+3)^{2} &=4 \\\y &=x-3\end{aligned}$$

Will help you prepare for the material covered in the next section. $$\text { If }\left(x_{1}, y_{1}\right)=(-3,1) \text { and }\left(x_{2}, y_{2}\right)=(-2,4), \text { find } \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

Solve by the quadratic formula: \(5 x^{2}-6 x-8=0\) (Section P.7, Example 10)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.