Which Equation Represents a Line Parallel to 3y-1=2x?

  • Context: MHB 
  • Thread starter Thread starter flnursegirl
  • Start date Start date
  • Tags Tags
    Lines Parallel Slope
Click For Summary
SUMMARY

The equation representing a line parallel to the graph of 3y - 1 = 2x is derived by determining the slope of the original line, which is 2/3. The provided options were analyzed using the slope-intercept form (y = mx + b). The correct answer is identified as option B: -2x + y = 6, which simplifies to y = 2x + 6, yielding a slope of 2, not matching the required slope of 2/3. The discussion concludes that none of the provided equations correctly represent a parallel line.

PREREQUISITES
  • Understanding of slope-intercept form (y = mx + b)
  • Ability to manipulate linear equations
  • Knowledge of parallel line properties
  • Familiarity with basic algebraic operations
NEXT STEPS
  • Study the properties of parallel lines in coordinate geometry
  • Practice converting linear equations to slope-intercept form
  • Explore common mistakes in algebraic manipulation
  • Learn how to verify the correctness of solutions in linear equations
USEFUL FOR

Students learning algebra, educators teaching linear equations, and anyone preparing for standardized math tests.

flnursegirl
Messages
8
Reaction score
0
The graph of which of the following equations is a straight line parallel to the graph of 3y-1=2x?
A: -3x + 2y = -2
B: -2x + y = 6
C: -2x + 2y = 3
D: -x + 3y = -2

Can you show the work when you answer please? Thanks
 
Mathematics news on Phys.org
flnursegirl said:
The graph of which of the following equations is a straight line parallel to the graph of 3y-1=2x?
A: -3x + 2y = -2
B: -2x + y = 6
C: -2x + 2y = 3
D: -x + 3y = -2

Can you show the work when you answer please? Thanks
Usually we ask you to show your work, so we can see where you got stuck.

There are a number of ways to find the slope of a line in the plane-which ones do you know?
 
Using y=mx+b I got y=2/3x+1 for the first line.

For choice A I got y=3/2x-2
For choice B I got y=2x+6 (the key says this is the answer)
For choice C I got y=1x=3
For choice D I got y=1/3x-2

None of these look correct to me using this method.
 
flnursegirl said:
Using y=mx+b I got y=2/3x+1 for the first line.

For choice A I got y=3/2x-2
For choice B I got y=2x+6 (the key says this is the answer)
For choice C I got y=1x+3
For choice D I got y=1/3x-2

None of these look correct to me using this method.
That's a good method, and none of the answers give the same "$m$" value, so it appears your text has a typo. You should use parentheses when you use the "/" symbol, so no one confuses

y = 3/2x - 2, whereby you mean: y = (3/2)x - 2 with:

y = 3/(2x - 2).
 

Attachments

  • IMAG00228.jpg
    IMAG00228.jpg
    67.1 KB · Views: 114
Hey flnursegirl! ;)

I agree with your method and with Deveno - none of the given answers is correct.
 

Similar threads

MHB What Is the Correct Equation for the Tangent of a Circle at a Given Point?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Why I Get X & Y Mixed Up When Plotting Graphs
  • · Replies 3 ·
Replies
3
Views
2K
High School Solving the Heart Curve Equation: 'y =
  • · Replies 18 ·
Replies
18
Views
4K
MHB Finding lines through given point perpendicular and parallel to given line
  • · Replies 1 ·
Replies
1
Views
1K
MHB Slope Intercept Equation with parallel
  • · Replies 2 ·
Replies
2
Views
1K
MHB Math Cumulative Review: Find the equation of a Line
  • · Replies 2 ·
Replies
2
Views
2K
Prove that these three ratios are equivalent
  • · Replies 11 ·
Replies
11
Views
2K
MHB Rearranging formula 3y + x = -1
  • · Replies 1 ·
Replies
1
Views
1K
MHB [ASK] A Line Intercepting A Circle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Circle a equation in a straight line
  • · Replies 8 ·
Replies
8
Views
2K