SOLUTION: write the equation of the line that is parallel to the line y=-3x+1 and passes through the point (4,2) the answer i got is 3x+y=14 i want to know if this is right

Algebra ->  Equations -> SOLUTION: write the equation of the line that is parallel to the line y=-3x+1 and passes through the point (4,2) the answer i got is 3x+y=14 i want to know if this is right      Log On


   

Question 328523: write the equation of the line that is parallel to the line y=-3x+1 and passes through the point (4,2)
the answer i got is 3x+y=14
i want to know if this is right
Found 3 solutions by Fombitz, solver91311, nyc_function:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see parallel lines have equal slopes.
y=-3x%2Bb Use the point (4,2) to solve for b.
2=-3%284%29%2Bb
b=14
y=-3x%2B14
highlight%283x%2By=14%29
Looks right.
Good job!

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Except for a tiny error in semantics, you are spot on. In point of fact, you cannot answer the question that was posed in the way it is posed. "Write the equation of a line" is impossible. In fact, there are an infinite number of equations that represent the set of ordered pairs for any given line. What you wrote, and correctly, was an equation of the line parallel to through .

To prove that it is impossible to write the equation of a line, I only have to show that there is more than one way to write such an equation.

where

where



are all representations of the same set of ordered pairs.


John

Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
For the perpendicular line, I have to find the perpendicular slope.
Look at your equation. Do you see -3 next to x? This is the slope of the given equation.
However, the line we are searching must have a slope that is the negative reciprocal of -3. What is the negative reciprocal of -3?
In other words, what fraction when multiplied by -3 will produce -1?
The negative reciprocal slope of the equation we want to find is 1/3 because -3 times 1/3 = -1.
We now use the given point (4,2) and 1/3 in the point-slope formula.
y - y1 = m(x - x1)...his is the point-slope formula.
y - 2 = 1/3(x - 4)
y - 2 = (1/3)x - 4/3
y = (1/3)x - 4/3 + 2
y = (1/3)x + 2/3
Done!
NOTE: The equation y = (1/3)x + 2/3 can also be written as y = (x + 2)/3. They both mean the same thing.