MHB Finding the Equation of a Line Given a Point and Slope

  • Thread starter Thread starter mathdad
  • Start date Start date
AI Thread Summary
To find the equation of a line that passes through the point (6, 2) with the same slope as the line represented by the equation 3x + 4y = 12, first solve for y to determine the slope. The slope from the equation is -3/4. Using the point-slope formula, substitute the slope and the point (6, 2) into the equation. This results in the equation y = (-3/4)x + 13/2. The final equation accurately represents the desired line.
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?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B Is Averaging Individual Slopes Equivalent to Linear Regression?
Replies
4
Views
2K
MHB What Is the Equation of a Line Parallel to 4x + 5y = 20 Passing Through (0,0)?
Replies
28
Views
4K
MHB Find an equation of the line that is perpendicular to x - y + 2 = 0
Replies
5
Views
2K
MHB How can I find the equation of a line given its x-intercept and y-intercept?
Replies
10
Views
2K
MHB Finding the Equation of a Line Given Two Points
Replies
2
Views
1K
MHB I have a few more questions.No problem, happy to help!
Replies
5
Views
2K
MHB Mechanics: Find Coefficient of Friction on 34° Slope w/ 0.4
Replies
9
Views
1K
MHB Finding the Equation of a Line through a Point and Circle Center?
Replies
2
Views
1K
MHB What is the equation of a line passing through (6, -3) with a y-intercept of 8?
Replies
4
Views
1K
MHB Finding the Equation of a Line with Point-Slope Formula
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top