Amrita Bhasin

verified

This problem has been solved

by verified expert Amrita Bhasin

100% free to try

Question

line through $(8,0)$ and perpendicular to the line $3 x+4 y=12$

   line through $(8,0)$ and perpendicular to the line $3 x+4 y=12$

Geometry

Ray C.… 1st Edition

Chapter 13, Problem 28

Instant Answer

Solved by Expert Amrita Bhasin

10/09/2019

Step 1

This gives us $y = -\frac{3}{4}x + 3$. Show more…

Show all steps

lock

Thanks for your feedback!

line through $(8,0)$ and perpendicular to the line $3 x+4 y=12$

Play audio

Feedback

Powered by NumerAI

Amrita Bhasin and 50 other subject Geometry educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conversion from Standard to Slope-Intercept Form

Many linear equations are presented in standard form (Ax + By = C), which can obscure the slope and y-intercept. Converting the equation into slope-intercept form (y = mx + b) directly reveals the slope (m) and the y-intercept (b), which are critical for graphing and analyzing the line's properties.

Perpendicular Lines

Perpendicular lines are two lines that intersect to form a right angle (90°). In coordinate geometry, if one line has a slope m, a line perpendicular to it will have a slope of -1/m. This negative reciprocal relationship is fundamental in determining the orientation of lines relative to each other.

Slope of a Line

The slope of a line quantifies its steepness and direction on a Cartesian plane. It is calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). Understanding slope is essential when analyzing the behavior of linear functions and when converting between different forms of linear equations.

Point-Slope Form

The point-slope form of an equation, expressed as y - y1 = m(x - x1), is used to write the equation of a line when you know one point on the line and its slope. This form is particularly useful for quickly determining the equation of a line under specific conditions, such as passing through a given point and being perpendicular to a given line.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace