Finding the Equation of a Line Given a Point and Slope

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

The equation of the line passing through the point (6, 2) with the same slope as the line defined by the equation 3x + 4y = 12 is derived using the point-slope formula. First, the given equation is rearranged to find the slope, which is -3/4. The point-slope formula is then applied, resulting in the final equation y = (-3/4)x + (13/2). This method confirms the accuracy of the calculations and the application of the point-slope formula.

PREREQUISITES
  • Understanding of linear equations and slope-intercept form
  • Familiarity with the point-slope formula
  • Ability to manipulate algebraic equations
  • Knowledge of coordinate geometry
NEXT STEPS
  • Study the derivation of the slope-intercept form from standard form equations
  • Practice using the point-slope formula with different points and slopes
  • Explore applications of linear equations in real-world scenarios
  • Learn about parallel and perpendicular lines in coordinate geometry
USEFUL FOR

Students, educators, and anyone interested in mastering linear equations and their applications in mathematics.

mathdad
Messages
1,280
Reaction score
0
Find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12.

1. Solve the given equation for y. The coefficient of x is the slope.

Yes?

2. I then plug the slope and given point into the point-slope formula and solve for y.

True?
 
Mathematics news on Phys.org
RTCNTC said:
Find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12.

1. Solve the given equation for y. The coefficient of x is the slope.

Yes?

Yes.

RTCNTC said:
2. I then plug the slope and given point into the point-slope formula and solve for y.

True?

That's one way to do it, so yes, that's true.
 
(6, 2) and 3x + 4y = 12.

3x + 4y = 12

4y = -3x + 12

y = (-3/4)x + 12/4

y = (-3/4)x + 3

The slope is (-3/4).

y - 2 = (-3/4)(x - 6)

y - 2 = (-3/4)x + (18/4)

y = (-3/4)x + (18/4) + 2

y = (-3/4)x + (13/2)

Correct?
 

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 Find an equation of the line that is perpendicular to x - y + 2 = 0
  • · Replies 5 ·
Replies
5
Views
2K
MHB How can I find the equation of a line given its x-intercept and y-intercept?
  • · Replies 10 ·
Replies
10
Views
3K
MHB Finding the Equation of a Line Given Two Points
  • · Replies 2 ·
Replies
2
Views
1K
MHB I have a few more questions.No problem, happy to help!
  • · Replies 5 ·
Replies
5
Views
2K
MHB Mechanics: Find Coefficient of Friction on 34° Slope w/ 0.4
  • · Replies 9 ·
Replies
9
Views
1K
MHB Finding the Equation of a Line through a Point and Circle Center?
  • · Replies 2 ·
Replies
2
Views
1K
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 Finding the Equation of a Line with Point-Slope Formula
  • · Replies 2 ·
Replies
2
Views
1K
MHB Friction Mechanics: Solving for Block's Speed at Point A
  • · Replies 1 ·
Replies
1
Views
1K