Find an equation of the line that is perpendicular to x - y + 2 = 0

  • Context: MHB 
  • Thread starter Thread starter mathdad
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around finding an equation of a line that is perpendicular to the line defined by the equation x - y + 2 = 0 and passes through the point (3,1). Participants explore the steps involved in deriving this equation, including different forms of the equation (slope-intercept and standard form) and the implications of using various methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant outlines a series of steps to find the perpendicular line, emphasizing the need to determine the negative reciprocal of the slope from the given equation.
  • Another participant questions whether the term "solve for y" should be replaced with "solve for b" in the context of the point-slope formula.
  • A later reply clarifies that the slope is necessary for the equation rather than the y-intercept, challenging the previous suggestion.
  • There is a discussion about the appropriateness of using point-slope form versus slope-intercept form, with some participants expressing a preference for slope-intercept as being easier to work with.
  • One participant provides a detailed breakdown of the steps, including solving for y and finding the negative reciprocal slope, ultimately arriving at the equation in standard form.

Areas of Agreement / Disagreement

Participants generally agree on the steps to find the equation, but there is disagreement regarding the terminology used (solving for y vs. b) and the preferred method for deriving the equation (point-slope vs. slope-intercept). The discussion remains unresolved on these points.

Contextual Notes

Some steps in the reasoning process may depend on the interpretation of the terms used, and there are unresolved questions about the best approach to take in deriving the equation.

mathdad
Messages
1,280
Reaction score
0
Find an equation of the line that is perpendicular to x - y + 2 = 0 and passes through the point (3,1). Write your answer in two forms: y = mx + b and Ax + By + C = 0.

The equation we want is perpendicular to the given equation. This means the slope must be the negative reciprocal of the slope of the given equation.

True?

Steps:

1. Solve the given equation for y.

2. Find the negative reciprocal slope of the equation in step 1.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

4. Express the equation in the form Ax + By + C = 0

Correct?
 
Mathematics news on Phys.org
For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)
 
greg1313 said:
For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)

Why solve for b in step 3? The slope m is required for the needed equation not the y-intercept or b.
 
Sorry; I mistook "point-slope" for "slope-intercept". At any rate, I don't see why you'd use point-slope when slope-intercept and standard form are required. Also, slope-intercept seems easier to work with.
 
Cool.
 
Steps:

1. Solve the given equation for y.

x - y + 2 = 0

x - y = - 2

- y = - x - 2

y = (- x - 2)/(-1)

y = x + 2

2. Find the negative reciprocal slope of the equation in step 1.

The negative reciprocal of 1 is - 1. This is our slope.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

y - 1 = -(x - 3)

y - 1 = - x + 3

y = - x + 3 + 1

y = - x + 4

4. Express the equation in the form Ax + By + C = 0.

x + y - 4 = 0
 

Similar threads

MHB What Is the Equation of a Line Parallel to 4x + 5y = 20 Passing Through (0,0)?
  • · Replies 28 ·
Replies
28
Views
4K
MHB Finding the Equation of a Line Given a Point and Slope
  • · Replies 2 ·
Replies
2
Views
2K
MHB What is the equation of a line passing through (6, -3) with a y-intercept of 8?
  • · Replies 4 ·
Replies
4
Views
1K
MHB How can I find the equation of a line given its x-intercept and y-intercept?
  • · Replies 10 ·
Replies
10
Views
3K
MHB I have a few more questions.No problem, happy to help!
  • · Replies 5 ·
Replies
5
Views
2K
MHB Math Cumulative Review: Find the equation of a Line
  • · Replies 2 ·
Replies
2
Views
2K
MHB Find the equation of the line through (-9, 2); perpendicular to y= -1
  • · Replies 6 ·
Replies
6
Views
2K
MHB Finding the Equation of a Line with Given Slope and Y-Intercept
  • · Replies 4 ·
Replies
4
Views
2K
MHB What is the equation of a line with a slope of 0 and a y-intercept of 14?
  • · Replies 4 ·
Replies
4
Views
1K
MHB How do I find an equation of the line with a given x-intercept and point?
  • · Replies 5 ·
Replies
5
Views
2K