Expert: Wei Chong - 5/28/2008

Question
I'm doing Algebra homework, and it says:
A line passes through the points (4,6) and (-3,5). What is the equation of the line in standard form?

A. 7x-y=-38
B. x-7y=-38
C. x-7y=38
D. x+7y=38

I don't understand this, please do explain.
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Answer
Hi Rica,

Usually, it is recommended to get the equation of the line in slope-intercept form first. Then, convert it to standard form.

By doing so, you can save yourself from memorizing all those formulas for line equation. So, let me cover the basics first.

The math video in the page below shows how you can determine equation of a line in slope-intercept form (scroll down to watch video).

http://www.mathexpression.com/equation-of-a-line.html

Now, after understanding that, let's solve your question step-by-step. We know that slope-intercept form for a line is given as:

   y = mx + b  

Where m = slope and b = y-intercept. So to get the equation of the line, we need to find m and b. So let's:

1) Find m.
Let:
  (x1,y1) = (4,6)
  (x2,y2) = (-3,5)

So,
m = (y2-y1)/(x2-x1)
 = (5 -6)/(-3-4)
 =  -1/(-7)
 = 1/7

So now we have the equation as:
  y = (1/7)x + b  -----(1)

Next we need to find b,

2) Find b.

Substitute the point (4,6) into (1)
(this means y = 6 and x = 4)

y =(1/7)x + b
=> 6 = (1/7)(4) + b
=> 6 = 4/7 + b
=> 6 -4/7 = b
=> 38/7 = b

With b = 38/7, we have the equation of the line as:
  
  y = (1/7)x + 38/7   ----(2)

We can get rid of the denominator,7, by multiplying (2) with 7. Hence we have

  7*y = 7*[(1/7)x + 38/7]
=> 7y =  x + 38

So, to get the standard form, we just need x to be at the left hand side(LHS).

7y =  x + 38  (add -x to both sides)
=> 7y -x = 38   (multiply -1 to both sides)
=> x -7y = -38

So the answer is B.

Hope this helps.

Best Regards,
Wei Chong