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Write an equation in standard form of the line that passes through the point (6, -4) and has slope 1/2 .

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3 Answers

The Standard Form for a linear equation is Ax + By = C (A ≥ 0)

Because we have coordinates of a point on the line and slope, let's use Point-Slope Form of linear equation

y - y1 = m(x -x1)

y - (- 4) = (1/2)(x - 6) 

y + 4 = (1/2)x - 3

y - (1/2)x = - 3 - 4

Let's multiply both sides of equation by (- 2)

x - 2y = 14

~~~~~~~~~
6 - 2*(- 4) = 14
6 + 8 = 14
   14 = 14

Comments

Hi Nataliya;
Welcome to the conversation!
I researched this on Khan University.  You are correct.  This is the standard format the instructor is looking for.  The format David and I used is called slope-intercept.  You also used the point-slope format.
I never knew there were so many names for the equal but different concepts.
Y = mX + b  / Slope intercept form
 
  mx - y = -b  / Standard form
 
1/2 X - Y = - b
 
1/2 ( 6 ) - ( -4 ) = -b
 
7 = -b     b = -7
 
1/2 X - y =  7
 
   X - 2Y = 14 / Answer
    Just change the Slope intercept form to Standard form Straight.

Comment

Hi Summer;
This is standard form equation for a line...
y=mx+b
m=slope..This is (y2-y1)/(x2-x1)--The change of y divided by the change of x.  Some will call it rise over run.
b=y-intercept.  This is the value of y when x=0.
 
y=mx+b
y=(1/2)x+b
 
Let's plug-in the one point provided...
-4=(1/2)(6)+b
-4=3+b
Let's subtract 3 from both sides to isolate b...
-3-4=3+b-3
-7=b
 
y=(1/2)x-7
 
I hope this helps.  If not, please let me know.

Comments

Thank you so very much it's a shame I get it more now than i do in class but unfortunately it says that this is the wrong answer the answer choices are 
1. 6x + y = 7
2.1/2x − y = 24
3. 2x − y = 7
4.1/2x + y = 8
5. y =1/2x + 7
6. 2x + y = 6
7. 2x − y = 12
8. x − 2y = −14
 
I am very confused :(
 
Hi Summer;
Please do not be confused.  If it takes all night, we are all here to help you.
Carefully proofread everything.  There is a typographical error someplace.
I will wait for your response.
If we do not find the typographical error, then the instructor made a mistake.  It happens.
 
 
Hi Summer...I don't see the right answer here either.  Are you sure choice 8 isn't
x-2y=14?
That would be the same equation as y=1/2x-7
I copied and pasted the problem on here and I tried 8 and turns out it was right she just typed it in wrong, thanks you all so much!
Very good Summer!  Glad you found her mistake!
Hello again Summer,
 
After reading Nataliya's answer I think that is important that you know that y = mx + b for a linear equation where m is the slope and b is the y-intercept will give you y = 1/2x -7 that both Vivian and I got for an answer for the point (6, -4) on that line with a given slope of 1/2.  Since each element of an equation can be multiplied or divided by the same number and still be an equivalent equation Nataliya multiplying each element -2 to get 2y = x - 14 and then rearranging to x - 2y = 14 to get it into standard format works well.
Hi Again Summer;
I would like to add one more thing to Nataliya D.'s solution.
She multiplies both sides by -2.  As she initially explains, "The Standard Form for a linear equation is Ax + By = C (A ≥ 0)".  To render A equal or greater than zero, she performed this task.
Are you still confused?

Comment

y=mx +b where m is given at 1/2
 
substitute the point (6,-4)
 
-4= (1/2)6 +b
-4=3+b
b=-7
Equation would be y=1/2x -7

Comments

Hi David;
The 4 provided is negative.
Thanks Vivian...You got me this time!

Comment