SOLUTION: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-6,4) and is parallel to the line x-3y=6

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-6,4) and is parallel to the line x-3y=6      Log On


   

Question 1134499: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-6,4) and is parallel to the line x-3y=6
Found 3 solutions by mathsolverplus, MathLover1, ikleyn:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
Let's first find the slope of x-3y=6:
-3y=-x+6
y=(1/3)x-2
Slope = 1/3
Parallel means that our line is going to have a slope that is negative reciprocal to (1/3), which becomes -3
y=-3x+b substitute (-6,4) into this equation to find b
4 = 18 +b
b = -14
y=-3x-14
Convert this equation into standard form,
3x+y=-14



Want more additional instant FREE math help? Please check out and follow us on social media!!
Instagram (@mathsolver.plus) : https://www.instagram.com/mathsolver.plus/
Twitter (@MathSolverPlus): https://twitter.com/MathSolverPlus
Snapchat (@mathsolverplus)
Email: mathsolverplus@gmail.com

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line that satisfies the given conditions:
Contains the point (-6,4) and is parallel to the line+x-3y=6
first, recall that parallel lines have same slope
so, find a slope of the line+x-3y=6
+x-3y=6.......solve for y
+x-6=3y
y=x%2F3-6%2F3
y=%281%2F3%29x-2=> slope is m=1%2F3
since we have point and slope, use point slope formula to find equation

y-y%5B1%5D=m%28x-x%5B1%5D%29........plug in slope 1%2F3 and x=-6 and y=4 coordinates of given point

y-4=%281%2F3%29%28x-%28-6%29%29
y-4=%281%2F3%29%28x%2B6%29
y-4=x%2F3%2B6%2F3
y-4=x%2F3%2B2
y-4-x%2F3=2
y-x%2F3=2%2B4
-x%2F3%2By=62%2B4=> the final equation in standard form




Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by @mathsolverplus is fatally WRONG.

            The solution by @MathLover1 is fatally WRONG, too.

            I came to provide a correct solution. 


Each line parallel to the line x - 3y = 6 has THE SAME left side 


    x - 3y = c,      (1)


where "c" is the constant term.


To determine the constant value of "c", use the condition that the point (-6,4) belongs to the line  (1).


For it, substitute the coordinates x= -6,  y= 4 into equation (1) and calculate "c". You will get


    -6 - 3*4 = c = -6 - 12 = -18.


Thus your final equation is


    x - 3y = -18.       ANSWER

Solved, completed and answered.

------------------

For this and many other similar problems see the lessons
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point

    - OVERVIEW of lessons related to the slope of a straight line
in this site.

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.